Wave Racer CER Bellringer Wave Racer Bellringer
Daily Speed Check: CER Challenge
Name:
Date:
The Pit Crew Report
The speed of sound at the track is constant (340 m/s).
Nitro: Low-frequency rumble (50 Hz).Sonic: High-frequency whine (500 Hz).
Nitro
Sonic
Prompt: Which car produces sound waves with a shorter wavelength? Support your claim using CER.
C Claim
Starter: I claim that [Car Name] produces...
E Evidence
Starter: Based on the report, Sonic's frequency is... while Nitro's is...
R Reasoning
Starter: Since wave speed is constant, as frequency increases...
Objective: Analyze wave relationships (f, λ, v)
MS-PS4-1 | Wave Racer Series
Hands-on Wave Tasks Challenge
WAVE ACTION CHALLENGE
Hands-on Tasks
Name:
Date:
Orders: Do the "Action Task" at each station before the math problems. These are physical tests of your wave skills!
1
The Wave Builder
Finding Amplitude
The Task: Use the slinky. Make a steady wave. Have a partner place markers on the floor at the Center Line and at the Top (Crest).
Measure It:
Distance:
cm
This represents the: _________________________
Draw your wave here
2
The Human Timer
Rhythm & Timing
The Task: One person watches the clock for 10 seconds . The other person taps the desk at a steady pace. Count the taps.
Total Taps
_____
Taps Per Sec
_____
Secs Per Tap
_____
Challenge: Can you hit exactly 25 taps in 10s? Circle: YES / NO
3
The Wave Speed Trap
How Fast Is It?
The Task: Stretch the slinky to 2 meters . Time how long a single pulse takes to travel the whole way.
Dist: 2.0m Time: _____ s
Speed (dist / time): _____ m/s
Try it 3 times and take the average!
4
The Grid Challenge
Drawing Precision
The Task: Draw a wave that is: 2 squares tall and 8 squares long .
Precision Grid
"The distance from your first top to your first bottom should be exactly 4 squares!"
5
The Echo Challenge
Sound & Reflection
The Task: Stand 5m from a wall. Clap once. Listen for the sound to bounce back.
Why do we divide by 2 for echoes?
Echo Rule
d = v · t / 2
Wave Action Module // Lab Series
Progress:
Wave Anatomy Reading Wave Anatomy
Deriving the Mathematical Language of Motion
UNIT: MECHANICAL WAVES
PHY-WAVE-001
Name
Date
The Wave Function
In physics, a wave function , denoted as \(y(x,t)\), describes the displacement of a medium at any position (\(x\)) and time (\(t\)). It maps out the shape and motion of a wave.
Step 1: The Snapshot (\(t=0\))
Imagine a wave frozen at \(t=0\). A harmonic wave follows a sine curve: \(y(x, 0) = A \sin(kx)\).
\(A\) is the amplitude . \(k\) is the wave number , defined as:
\(k = \frac{2\pi}{\lambda}\)
y x \(\lambda\) A
Step 2: Adding Motion
To model a wave moving right at velocity \(v\), we replace \(x\) with \((x - vt)\). This gives us:
\(y(x, t) = A \sin(k(x - vt))\)
Step 3: Angular Frequency
Distributing \(k\) gives \(y(x,t) = A \sin(kx - kvt)\). The term \(kv\) simplifies to \(2\pi f\), known as angular frequency (\(\omega\)).
\(kv = \frac{2\pi}{\lambda} \cdot \lambda f = 2\pi f = \omega\)
General Wave Function
\(y(x, t) = A \sin(kx - \omega t + \phi)\)
A
Amp
k
Wave No.
ω
Ang Freq
φ
Phase
Mission Debrief
1. Wavelength Calculation: Find the wave number \(k\) for \(\lambda = 4 \, m\). Show your steps.
2. Concept Check: Why is \((x - vt)\) used for a wave moving right instead of \((x + vt)\)?
3. Analyze: \(y(x, t) = 5 \sin(3x - 12t)\). Identify the following:
Amplitude
Wave Number (\(k\))
Angular Freq (\(\omega\))
Wave Speed (\(v\))
© 2026 Wave Runners • PHY-001
Interference Blueprinting Activity Interference Blueprinting
Wave Runner Engineering Series: Station 06
Classification: Field Data
Name:
Date:
The Principle of Superposition
When two waves overlap, their amplitudes add together at every point. This is interference . Your mission is to predict the "Resultant Wave" by adding the displacement of Wave A and Wave B at every grid line.
Constructive
Crests line up with crests. Waves grow larger.
Destructive
Crests line up with troughs. Waves cancel out.
Challenge 01: Mega-Pulse
Constructive
0 +1 +2 -1 -2 WAVE A (+2) WAVE B (+2)
Task: Draw the **Resultant Wave** in solid black. Use the sum of A + B at every grid line.
Peak Amp A:
Peak Amp B:
Challenge 02: Ghost Wave
Destructive
0 +1 +2 -1 -2 WAVE A (+2) WAVE B (-2)
Resultant Midpoint Calculation (Show Work):
Challenge 03: Complex Overlap
Mixed Analysis
0 1 2 3 4 5 6 7 8 9 10 11 12
Point-by-point addition. At every numbered x-value, add heights.
Analysis Brief:
At which X-value (0-12) did the waves experience the most constructive interference? Use your graph to justify your answer.
Write justification here...
Acoustic Chase Lab Activity Acoustic Chase Lab
Protocol: WR-DO-SW-04
Name:
Materials
Smartphone (Tone Gen)
Smartphone (FFT App)
Elastic Runner (2m+)
Tape Measure
Stopwatch
Safety
Clear walk paths. Do not over-tension springs. moderate volume on speakers.
Phase 1: Doppler Dynamics
The Doppler Effect occurs when relative motion exists between a source and an observer. Approaching sources compress wave fronts, increasing frequency (\(f_{obs}\)). Receding sources stretch them, decreasing frequency.
Phase 2: Standing Architectures
Standing Waves form through interference of reflected waves in fixed systems. Patterns form at resonant frequencies . Points of zero vibration are nodes ; points of maximum vibration are antinodes .
Doppler Formula
\[f_{obs} = f_s \left( \frac{v}{v \mp v_s} \right)\]
Resonance Formula
\[\lambda = \frac{2L}{n}\]
Scaffolded Analysis
Example 1: Approaching Siren
Ambulance siren (\(f_s = 600\) Hz) at 20 m/s toward observer (\(v = 340\) m/s).
Calculation:
\(f_{obs} = 600 \times [340 / (340 - 20)]\)
\(f_{obs} = 600 \times [340 / 320] = \mathbf{637.5 \text{ Hz}}\)
Example 2: 3rd Harmonic
2m string with 3 antinodes. Calculate wavelength (\(\lambda\)).
Calculation:
\(n = 3\), \(L = 2\)
\(\lambda = 2(2) / 3 = 4/3 = \mathbf{1.33 \text{ m}}\)
1
Doppler Dash Procedure
Action
Position Observer with FFT app.
Courier walks toward Observer with 500 Hz tone.Observe and record max frequency peak.
Courier walks away. Record lowest peak.
Trial Observed \(f_{obs}\) Approaching Receding
Calculation Area: Courier Velocity (\(v_s\))
2
Standing Signal
Search for resonance by adjusting the frequency of the elastic runner (\(L\)). When clear lobes form, record the harmonic characteristics below.
Length (L):
meters
Sound Shield Lab Activity SOUND SHIELD LAB
Acoustic Interference Challenge
Engineer:
Sector:
Mission Briefing
Use destructive interference to map out "Quiet Zones" in a sound field. Calculate the path length difference required to cancel out sound waves using two synchronized sources.
01
Pre-Calibration Math
1. Room Environment
Temp (°C)
Sound Speed (m/s)
Formula: \( v = 331.4 + 0.6 \cdot T_c \)
2. Wave Selection
Freq. Target (Hz)
1000 Hz
Wavelength (m)
Half-Wavelength Difference (λ/2):
______ m
Alternative Kit
2 Smartphones / Tablets
Frequency Gen App
Meter Stick / Tape Measure
Masking Tape
02
Acoustic Setup
1. Place both phones on a flat surface, exactly 1.0 meter apart.
Phone A Phone B 1.0 m Distance Mapping Zone
Pro-Tip: If you hear "beats," the frequencies aren't matched. Ensure both are set to exactly 1000 Hz.
03
Acoustic Mapping Data
Map the destructive node
Walk slowly through the Mapping Zone. Listen for a spot where the volume dips significantly. Mark it with tape.
Dist to Phone A (d1)
_____ m
Dist to Phone B (d2)
_____ m
Path Diff |d1 - d2|
_____ m
Visual Observation Sketch
Sketch position vs. sources
Engineering Review
1. Verification Check: How close was your Path Difference to the predicted λ/2?
2. Systems Logic: If you moved Phone B further away, would the "Quiet Zone" move toward or away from Phone A?
3. Real World App: How does this experiment explain Noise Canceling technology?
Acoustic Engineering Division // MS-PS4-1
MOD 09-02-B
Harmonic Tension Reading Pack Harmonic Tension Pack
Physics Technical Brief: Standing Waves & Resonance
Module: Wave Runners
Name:
Date:
The Anatomy of a String Wave
When a string is stretched between two fixed points, waves travel back and forth, reflecting off the boundaries. When the frequency is "just right," these waves interfere with their own reflections to create a standing wave .
The speed at which a pulse travels down a string depends on Tension (T) and Linear Mass Density (μ).
Tension (T): Pulling force measured in Newtons (N). Often calculated as \(T = m \cdot g\).
Linear Density (\(\mu\)): Mass per unit length (kg/m). Often \(\mu = \frac{\text{mass}}{\text{length}}\).
Wave Speed (v): Velocity of the energy. Calculated as \(v = \sqrt{T/\mu}\).
Resonant Condition
Standing waves only occur when the string length is a multiple of half-wavelengths.
f_n = n · f_1
The Harmonic Sequence Modes of Vibration
1 Fundamental (n=1): One hump. Lowest possible frequency. \(\lambda = 2L\).
2 2nd Harmonic (n=2): Two humps (1 node in middle). \(\lambda = L\).
Fundamental (n=1) 2nd Harmonic (n=2)
Comprehension Check
1. If you increase the hanging mass on a string by 4 times, how does the wave speed change? Justify using the speed equation.
2. A string produces its fundamental frequency (\(n=1\)) at 20 Hz. Predict the frequency of the 4th harmonic (\(n=4\)).
Engineering Perspective
Would you want thick strings (high density) or thin strings (low density) for a bass guitar playing low notes? Explain your reasoning.
Moving Waves Slides v2 Moving Waves
The Science Discovery Lab
Today's Goal
Your goal is to learn the secrets of how waves move through different things.
Watch
Watch how waves travel through water and springs.
Change
Change the speed and size to see what happens.
Explain
Find the rules that all waves follow.
Activity 1: Slinky Fun
Side-to-Side
Give your Slinky a quick side-to-side snap. Does the metal move with the wave?
Push and Pull
Push the Slinky forward. How is this wave different from the side-to-side one?
Safety
Do not stretch the Slinky too far!
Activity 2: Water Ripples
"Faster tapping makes more waves..."
Tap the water gently.
Tap faster (Frequency).
What happens to the distance between waves (Wavelength)?
WAVE RULE
Frequency vs. Distance
Watch how the distance changes.
Time to Practice
Now that you've seen the waves, it's time to do the math.
Your Station Tools
Station Cards
The instructions and math problems. Look at the pictures for help!
Action Tasks
The hands-on challenges on your worksheet. Do this FIRST!
Worksheet
Where you write your answers. Show all your work!
Math Help
Wave Speed
Speed = Frequency × Wavelength
How fast energy moves
Timing
Freq = 1 / Time
How many per second
REMEMBER: Use SECONDS for Hertz! If you have minutes, multiply by 60.
Teacher Key
Action Tasks
Task 1: Measuring to the crest = AMPLITUDE.
Task 2: Hertz is the number of events in 1 SECOND.
Task 5: Divide echoes by 2 because sound goes there and back.
Math Key
Speed (v): Multiply Freq × Wavelength.
Period (T): Time for exactly one wave to pass.
Symmetry: Crest to Trough = 1/2 Wavelength.
Hands-on Wave Key Teacher Key
WAVE ACTION CHALLENGE KEY
Solutions & Teacher Notes
Unit: Wave Motion
1
The Wave Builder Key
Expected Answer:
The distance represents the: AMPLITUDE
Make sure students measure from the center line, not the bottom of the wave.
Why this task?
Students often think amplitude is the total height. Marking the middle line fixes this.
2
The Human Timer Key
Math Check:
• Taps per sec: Taps / 10
• Secs per tap: 1 / (Taps per sec)
25 taps = 2.5 Hz = 0.4s
Why this task?
Hertz can be a confusing word. This task shows it's just a count of how many things happen in one second.
3
The Wave Speed Trap Key
Formula:
Speed = Distance / Time
If the time is 0.5s, the speed is 4.0 m/s.
Why this task?
Shows that wave energy has a real speed that we can measure with a timer.
4
The Grid Challenge Key
Checkpoints:
• Height: 2 squares up/down from center.
• Length: 8 squares for one full cycle.
Why this task?
Forces students to be careful with their drawings. They must see that a half-wave is exactly half the length.
5
The Echo Challenge Key
Answer:
"Because the sound travels twice the distance (to the wall and back). We only want the distance to the wall, so we divide by 2."
Teacher Guide // Wave Action Module
Teacher Resource
Wave Anatomy Key Wave Anatomy Key
Teacher Resource • Unit: Mechanical Waves
Key
1 Wavelength Calculation
Solution
\(k = \frac{2\pi}{\lambda} = \frac{2\pi}{4} = \frac{\pi}{2}\)
2 Motion Logic
Replacing \(x\) with \((x - vt)\) represents a right-shift . As \(t\) grows, \(x\) must grow to keep the phase constant.
"Negative sign = Positive direction (Right)"
3 Component Analysis
\(y(x, t) = 5 \sin(3x - 12t)\)
Amp (A)
5
k
3
Ang Freq (ω)
12
Speed (v)
4 m/s
Calculation for speed: \(v = \omega / k = 12 / 3 = 4\)
Quick Reference
Symbol Meaning Unit k Wave Number (\(2\pi/\lambda\)) rad/m ω Angular Freq (\(2\pi f\)) rad/s v Velocity (\(\lambda f\)) m/s
© 2026 Wave Runners • Teacher Resource
Interference Impact Lab Activity Interference Impact Lab
Wave Runner Simulation Series: Lab 04
Subject: Physical Interference
Name:
Mission Briefing
Open the PhET Wave Interference simulation. Select the "Interference" tab and choose the Water icon.
phet.colorado.edu/sims/html/wave-interference/latest/wave-interference_all.html
Controls:
1. Toggle "Graph" view ON.
2. Toggle "Play" (Green button for both).
3. Use the Probe to measure amplitude.
1
Visual Pattern Mapping
A. The "Grey Lines" (Still Zones):
Sketch Probe Graph:
Constructive Destructive
B. The "Bright Dots" (Active Zones):
Sketch Probe Graph:
Constructive Destructive
2
Frequency Variable Test
Frequency Observation of Pattern Distance between Zones LOW HIGH
Prompt: How does wavelength change as you increase frequency, and how does this affect the pattern?
Synthesis: Tech Application
Noise-canceling headphones use a microphone to hear outside sound and then generate an "anti-noise" wave. Based on your lab results, what type of interference are they creating? Explain why the user hears silence.
Your explanation...
Sound Shield Lab Key SOUND SHIELD KEY
Teacher Facilitation & Answer Guide
MOD 09-02-B
Setup
Use identical web-based generators on both devices to avoid hardware variance that causes beats instead of static zones.
Tip
Students should close one ear and rotate their head slowly. Finding the "Node" (Quiet Spot) requires precise spatial alignment.
Site
Use open hallways. Hard classroom surfaces create reflections that muddle the constructive/destructive pattern.
01
Expected Data Example (@ 20°C)
Speed of Sound: 343.4 m/s
Frequency: 1000 Hz
Wavelength (λ): 0.343 m
Target Path Diff (λ/2): ~ 0.17 m (17 cm)
Geometric Logic:
With speakers 1.0m apart, a node found at:
Analysis Solutions
1. Verification
Answers vary based on precision. Students should note measurement error (measuring to the ear) is primary. Results within 2-3 cm of 0.17m are high precision.
2. Variable Change
The zone moves away from Phone A. To maintain the λ/2 difference, the observer must shift outward to compensate for the source being further away.
3. Noise Cancellation
Headphones use a mic to hear external noise, then a speaker plays the inverse wave (shifted by 180°, or λ/2). This cancels the noise at the eardrum.
Teacher Resource // Wave Runner Series
ANSWER KEY
Acoustic Chase Key Acoustic Chase Key
Teacher Reference: WR-DO-SW-KEY
Confidential Answer Key
Pedagogical Rationale
This lab sequence connects the dynamic Doppler Effect with stationary Standing Waves . Students often struggle with the difference between wave transfer and wave confinement . The Doppler Dash provides a physical sensation of frequency shift, while the Standing Signal requires careful manipulation to find discrete resonant states.
Example Walkthroughs
Example 1 (Doppler)
Result: 637.5 Hz
Ensure students use v − vs in the denominator (340 − 20 = 320). A common mistake is adding the velocity for an approaching source.
Example 2 (Harmonic)
Result: 1.33 m
Check that students identify 3 antinodes as the 3rd harmonic (n = 3 ). Use the formula λ = 2L / n .
Part 1: The Doppler Dash
Expected Lab Values
Typical brisk walk speed: 1.5 to 2.5 m/s .503 Hz (approach) and 497 Hz (recession).
Model Calculation (Approach):
503 = 500 × [343 / (343 − vs)]
Part 2: Standing Signal
Harmonic (n) Nodes Antinodes Wavelength (λ) n = 1 (Fundamental) 2 1 2L n = 2 Harmonic 3 2 L n = 3 Harmonic 4 3 2/3 L
Debrief 1: Velocity Logic
Teacher Key: Frequency shift (Δf) is directly proportional to source speed. If the courier doubles their speed, the shift from the source frequency (500 Hz) will also double (e.g., shifts to 506 Hz instead of 503 Hz).
Debrief 2: Energy States
Doppler: Kinetic energy is transferred through the medium from a moving source to a receiver.
Standing: Energy is confined and stored in the oscillating patterns (nodes and antinodes). No net energy is transferred through the medium.
Wave Racer CER Key Teacher Resource
Wave Racer CER Key
Frequency & Wavelength Relationships
Lesson: Wave Runners
Answer Key
Scenario Summary
Nitro (50 Hz) vs. Sonic (500 Hz). Speed is constant at 340 m/s. Students must identify which car has a shorter wavelength.
C
The Claim
"Sonic produces the sound waves with the shorter wavelength."
E
The Evidence
Sonic has a higher frequency (500 Hz) than Nitro (50 Hz).
Speed is constant (340 m/s) because the air medium is the same.
R
The Reasoning
Wave speed is defined as v = f × λ. Since the medium (air) does not change, the speed is constant. This creates an inverse relationship between frequency and wavelength.
As frequency increases, wavelength must decrease to maintain the same speed. Sonic's frequency is 10 times higher than Nitro's, so its wavelength must be 10 times shorter.
Nitro: λ = 340 / 50 = 6.8 m
Sonic: λ = 340 / 500 = 0.68 m
Common Misconceptions to Address
Thinking frequency changes wave speed (speed is only determined by the medium).
Believing frequency and wavelength are directly proportional (High f = High λ).
Failing to connect the math to the concept (not using the equation to support the inverse rule).
Rubric: Claim (1pt) | Evidence (1pt) | Reasoning (2pts)
MS-PS4-1 | Wave Racer Series
Standing Wave Scaffolds Activity Standing Wave Scaffolds
Technical Mission: Calculating Resonance & Tension
Wave Speed v = √(T / µ)
Name:
Date:
Case Study #01
Scenario: The Standard String
A string of length L = 1.40 m is attached to an oscillator and passes over a pulley. A 2.00 kg mass hangs from the end. The string linear density is µ = 0.004 kg/m.
1. Draw a Picture
Label components: Oscillator, Pulley, Mass, Length
2. List Variables
Mass (m)
Density (µ)
Length (L)
Gravity (g)
9.8 m/s²
3. Tension (T)
T = m · g
4. Wave Speed (v)
v = √(T / µ)
5. Fund. Freq (f1)
f1 = v / (2L)
Case Study #02
Scenario: The Heavy Tension
Replace the hanging mass with a 8.00 kg mass. All other variables stay the same. Calculate the new fundamental frequency (f1).
New Tension (T)
New Speed (v)
New Freq (f1)
Predict & Analyze
The mass increased by 4x. Did the frequency also increase by 4? Explain using the square-root relationship.
Case Study #03
Scenario: The Precision Harmonic
A string has a tension of 25.0 N and length 2.00 m. If the fundamental frequency (f1) is 12.5 Hz, find the linear density (µ).
Step 1: Find Wave Speed (v)
Step 2: Solve for Density (µ)
Harmonic Review
Resonances follow: fn = n · f1. Calculate:
2nd Harmonic (n=2)
Hz
3rd Harmonic (n=3)
Hz
Wave Runner Lab Series
Wave Practice Stations Station 1
Parts of a Wave
1. Find the wave parts for each number (1-3):
A B C D E F G 1 2 3
2. Which letters (A-G) show ONE full wave?
Help: Wave Parts
Example:
"If a wave is 10cm from one peak to the next, the wavelength is 10cm. If it is 3cm from the middle line to the top, the amplitude is 3cm."
Note: Wavelength is the length of one full cycle. Amplitude is how high or low the wave goes from the middle.
Science Core: Waves
WAVE PRACTICE
Station 2
Speed & Timing
A coach walks back and forth 10 times in 2 minutes. What is the frequency in Hertz?
If a wave takes 5.0 seconds for one cycle, what is the frequency in Hertz?
What is the timing for one cycle of a 440 Hertz sound wave?
A building sways back and forth with a frequency of 0.10 Hz. How long for one sway?
A hummingbird beats wings 70 times/sec. Frequency = ? If v = 350 m/s, Wavelength = ?
Help: Frequency
f = 1 / T | T = 1 / f
Example:
"If one cycle takes 0.25s, the period (T) is 0.25s. The frequency is 1 / 0.25 = 4.0 Hz."
Note: Frequency is how many cycles happen in one second. Period is how many seconds one cycle takes.
Pro-Tip: Always use SECONDS for Hertz!
Science Core: Wave Motion
WAVE PRACTICE
Station 3
The Wave Formula
A sound wave has f = 262 Hz and Wavelength = 1.29 m. Find Speed (v), Time to travel 91.4 m, and Period (T).
Find the speed of a wave with f = 2.5 Hz and Wavelength = 0.6 m.
A wave on a string travels at 15 m/s. If f = 5 Hz, find the Wavelength.
An ocean wave is 10m long and passes a buoy every 2 seconds. Find its speed.
Find the wavelength of a sound wave in water with Speed = 1531 m/s and f = 256 Hz.
Help: Speed = f · λ
Speed = f × Wavelength
Example:
"A wave has f = 10Hz and Wavelength = 0.5m. Speed = 10 × 0.5 = 5 m/s."
Note: Wave speed tells you how fast the energy is moving. It is the frequency times the wavelength.
To find travel time, use:
Wave Discovery Activity Wave Discovery Activity
UNIT: SCIENCE // TOPIC: HOW WAVES MOVE
Name:
Date:
Goal:
See how waves change when we move them in different ways.
1
Slinky Fun
Part A: Side-to-Side. Move your hand quickly side-to-side once. Watch the wave move.
Draw the wave and tell how your hand moved:
Part B: Push and Pull. Push the Slinky toward your partner. Watch the coils bunch up.
How is this different from the side-to-side wave?
2
Water Ripples
Tap the water surface at different speeds.
Slow Tapping
What is the distance between ripples?
Fast Tapping
What is the distance between ripples?
Big Question
When you tap faster, do the ripples get closer together or farther apart? Write your wave rule here:
3
Waves Meeting
Both partners send a wave at the same time. Watch when they meet.
The Meeting: What happened when the waves crossed?
Afterwards: Did they bounce back or keep going?
What We Learned
Tell how waves carry energy without moving the object itself. Use words like: Energy, Pulse, Speed, Waves.
Wave Practice Answer Key Wave Practice Answer Key
Teacher Solutions
OFFICIAL KEY
Station 1: Wave Parts
1. Parts: 1 = Wavelength | 2 = Amplitude | 3 = Wavelength
2. Sequence: A-E , B-F , or C-G (One full wave).
Station 2: Speed & Timing
4. 10 cycles / 120s = 0.083 Hz
5. 1 / 5.0s = 0.2 Hz
6. 1 / 440Hz = 0.00227 s
15. 1 / 0.10Hz = 10 s
22. f = 70 Hz ; Wavelength = 350/70 = 5 m
Station 3: Wave Formula (Speed = f × Wavelength)
10. Sound Wave: Speed = 262 × 1.29 = 337.98 m/s ; Time = 91.4 / 337.98 = 0.27 s ; Period = 1/262 = 0.0038 s
13. Speed = 2.5 × 0.6 = 1.5 m/s
14. Wavelength = 15 / 5 = 3 m
16. Speed = 10m / 2s = 5 m/s
21. Wavelength = 1531 / 256 = 5.98 m
Station 4: Highs & Lows
3. Period: T = 1 / 51.2 Hz = 0.0195 s
8. Wave Math:
Amplitude: 32/2 = 16 cm
Wavelength: 48 × 2 = 96 cm (0.96m)
Period: 1/2.4 = 0.417 s
Speed: 2.4 · 0.96 = 2.304 m/s
9. Ocean Waves:
Amplitude: 4.6/2 = 2.3 m
Frequency: 1 / 6.2s = 0.161 Hz
Speed: 0.161 · 8.6 = 1.385 m/s
Station 5: Echoes & Sound
7. Time: 20 / 340 = 0.059 s
11. Chime: Speed = 515 / 1.5 = 343.3 m/s ; Period = 1/436 = 0.0023 s
12. Echo Rule: Total dist = 1370 m.342.5 m/s .456.7 Hz .
Standing Wave Master Key Standing Wave Master Key
Teacher Resource // Wave Runners Lesson
Answer Sheet Confidential / Educator Only
Theoretical Foundation Key
1. Effect of increasing mass by 4x:
The wave speed will double . Since speed (v) is proportional to the square root of tension (T), increasing the mass by 4x increases the tension by 4x. Because of the square root, the speed increases by a factor of √4 = 2.
2. Harmonic Prediction (f1 = 20 Hz):
f4 = 4 · f1 = 4 · 20 Hz = 80 Hz.
Engineering Challenge Solution
Designers use high linear mass density . A "heavy" string (higher µ) travels waves slower. A slower speed results in a lower fundamental frequency for a given string length and tension, allowing for deep bass notes without requiring impractically long strings.
Mission Analysis Keys
01 Standard String (2.00 kg)
Tension (T)
19.6 N
2.00 · 9.8
Speed (v)
70 m/s
√(19.6 / 0.004)
Freq (f1)
25 Hz
70 / (2 · 1.40)
02 Heavy Tension (8.00 kg)
Tension (T)
78.4 N
8.00 · 9.8
Speed (v)
140 m/s
√(78.4 / 0.004)
Freq (f1)
50 Hz
140 / 2.8
Harmonics
n=2100 Hz
n=3150 Hz
03 Precision Density
Step 1: Speed
v = 12.5 · (2 · 2.00) = 50 m/s
Step 2: Density (µ)
µ = 25 / (50)2 = 0.01 kg/m
Strategy Note
Ask students if doubling the frequency means the tension doubled. They will likely say yes. Use Case Study #2 to prove that frequency only doubled when tension (mass) quadrupled.
Setup Tip
Remind students to always convert mass to Newtons (N) by multiplying by 9.8. Many students plug kg directly into the velocity formula which results in an incorrect wave speed.
Wave Video Quiz Sheet Wave Video Quiz
Watching: Wave Motion by FuseSchool
NAME:
DATE:
1. All waves move ________ from one place to another without moving any matter.
A) People
B) Energy
C) Water
D) Air
2. In the "stadium wave" example, do people move to a new seat for the wave to travel?
Yes
No
3. Can waves travel through empty space (a vacuum)?
Yes
No
Frequency Definition:
"The number of complete waves passing a fixed point in a given amount of time (usually one second)."
Unit
HERTZ
(Hz)
4. Frequency is how OFTEN a wave happens. What is the word for the TIME it takes for one wave to pass?
5. Wavelength is the distance between one point on a wave and the same point on the next wave.
Example: Peak to Peak distance.
Draw the Wavelength symbol (\(\lambda\)) here:
6. What is amplitude?
The total length of the wave
The distance from the center line to the maximum top
The speed at which the wave moves
7. Think about the "Flat Sea." When a wave comes, the maximum height it reaches from that flat spot is its ________.
Answer Here
Video Series // Wave Motion
Sound Properties Lab Activity Sound Properties Lab
Pit Crew Sound Diagnostic
Name:
Date:
Mission Briefing
Sound is a longitudinal wave that transfers energy through vibrations. In this lab, you will use a "Salt Drum" to see how sound energy physically moves through a medium.
The "Salt Drum" Tech Specs
What is it? A visualizer that converts sound vibrations into physical motion.
How it's made: Stretch plastic wrap tightly over a bowl and secure it with a rubber band. Sprinkle salt on top. The plastic acts as a membrane that vibrates when sound waves hit it.
1
Engine Pitch Diagnostic
Procedure:
Compare three different sized tuning forks.
Strike each and observe the pitch.
Record your observations in the log.
Fork Size Pitch (High/Low) Smallest Medium Largest
Diagnostic Analysis: How does size affect frequency?
2
Exhaust Volume Check
Strike a tuning fork and hold it near (but not touching) the salt drum. Compare a gentle strike vs. a hard strike. Sketch the displacement (height) of the salt's movement.
Gentle (Soft)
Sketch Here
Hard (Loud)
Sketch Here
Energy Analysis: How does loudness relate to wave energy?
3
Medium Relay Test
Listen to a partner's tap through air vs. through the table (solid).
Through Air:
Through Solid:
Diagnostic: Why is sound louder through a solid?
Final Inspection
If a race car engine speeds up, its pitch increases. What is happening to the frequency and wavelength of the sound waves? Explain your reasoning.
Topic: Properties of Sound (Longitudinal)
Sound Properties Lab | Unit: Wave Runners
String Wave Lab Worksheet String Wave Lab
PHY-LAB-02 • Wave Runners
Investigator
Date
[X]PULSE
[X]NO END
[X]SLOW MO
[X]NO DAMP
[X]RULER
[X]REF LINE
1. Amplitude Variable
Amp (cm) Time (6cm) Speed 1.00 0.50 0.25
2. Pulse Width (λ)
Width (s) Wavelength Time (6cm) 1.00 0.50 0.25
3. Medium Tension
Tension Amp (cm) Width (s) Time (6cm) Speed HIGH 1.00 1.00 MED 1.00 1.00 LOW 1.00 1.00
4. Model Diagram
Draw and label: Amplitude, Wavelength (λ), Frequency, Speed, and First Particle Velocity.
Analysis Questions
1. Relationship Check: Does changing Amplitude affect Wave Speed? Support with evidence.
2. Medium Check: How does Tension affect Wave Speed? Explain the physical reason.
3. Limits of Model: What assumptions does the "No Damping" setting make about energy loss?
Wave Runners Series • Laboratory Protocol 02
Interference Master Key Teacher Master Key
Interference Blueprinting & Impact Lab
Internal Use Only
Pedagogical Resource
Interference Blueprinting Guide
Challenge 01 & 02: Basics CONSTRUCTIVE & DESTRUCTIVE
01 Constructive:
Resultant is a double-height wave (+4 units peak). Verify students aren't shifting the phase.
02 Destructive:
Resultant is a flat line at y=0. Common error: Squiggly lines instead of flat.
Challenge 03: Complex Overlap Solution Logic
Most Constructive: At x=2 (where Pulse A = +2 and Pulse B = +1). Resultant = +3.
Most Destructive: At x=6 (where Pulse A = -2 and Pulse B = +0.5). Resultant = -1.5.
Impact Lab Response Key
Still Water Zones:
DESTRUCTIVE
Probe graph should show a near-flat line. These are nodes .
Active Water Zones:
CONSTRUCTIVE
Probe graph should show high amplitude. These are antinodes .
Frequency Variable Analysis:
Increasing frequency decreases wavelength, as shown by the wave equation: \[ \lambda = \frac{v}{f} \]
Shorter wavelengths cause the interference peaks and valleys to occur closer together in space.
Observation: Nodal lines (grey zones) become more numerous and tighter together.
Synthesis & Applications
Noise-Canceling Tech:
The headphones produce "anti-noise" which is a wave 180° out of phase with the background noise. This creates destructive interference , resulting in a net amplitude of zero (silence) for the listener.
Student Standing at +10cm/-10cm Collision:
The student feels nothing . The net displacement is zero.
10m Intro 15m Blueprint 25m Lab 10m Debrief
60 Minute Session
Wave Crossings Activity WAVE CROSSINGS
Venn Analysis: Transverse vs. Longitudinal
Name:
Date:
Crests & Troughs
Compressions
Rarefactions
Transfers Energy
Frequency
Wavelength
Perpendicular
Parallel
Sound Waves
Light Waves
Amplitude
Seismic P-Waves
Seismic S-Waves
Requires Medium
Oscillates
Reflects/Refracts
Transverse Longitudinal Both
Technical Brief: Seismic Connection
P-waves arrive before S-waves. Explain why these wave types travel at different speeds through Earth.
Wave Runner // crossings analysis
MS-PS4-1 | TEKS 1G
Wave Practice Worksheet Wave Practice Sheet
Station Worksheet
Name:
Date:
Station 1
Wave Parts
Look for the repeating pattern.
P1: Identification (Find parts 1-3)
1:
2:
3:
P2: ONE Full Wave (Letters A-G)
Answer:
Station 2
Speed & Timing
Use seconds for Hertz!
P4: 2 Minutes
f = 10 / ______ s
Ans: ______ Hz
P5: 5.0s Period
f = 1 / 5.0
Ans: ______ Hz
P6: 440 Hz fork
T = 1 / 440
Ans: ______ s
P15: Sears (0.1Hz)
T = 1 / 0.10
Ans: ______ s
P22: Bird (70 beats/sec)
Freq (Hz):
Wave Length:
Station 3
Wave Formula
Speed = Frequency × Wavelength.
P10: Sound (f=262, Wavelength=1.29)
1. Speed (v)
2. Time (91.4m)
3. Period (T)
P13 & P14: Math Work
P13
P14
P16 & P21: Math Work
P16
P21
Station 4
Highs & Lows
Top to bottom = 1/2 wavelength.
P3: Wire Period
Freq = 51.2 Hz
Ans: ______ s
P8: Spring Wave Math
Amplitude
Wavelength
Period
Speed
P9: Ocean Waves
Find Frequency
Find Speed
Station 5
Echoes & Sound
Speed = (2 × Distance) / Time.
P7 & P11: Moving Waves
P7 TIME
P11 SPEED
P12: Echo Challenge (x2 Distance!)
Speed
Freq
Period
P17 & P18: Lake & Light
P17
P18
P19 & P20: Sonar & Pulse
P19
P20
Wave Practice Sheet: Station Activity
Did you show your units? (m, s, Hz, m/s)
Wave Discovery Answer Key Teacher Key
Wave Discovery Answer Key
Reference for Wave Discovery Activity Observations
1
Slinky Fun
Part A: Side-to-Side
Hand moves side-to-side. The wave travels forward. Coils return to start.
Part B: Push and Pull
Hand moves forward and back. Pulse looks like a bunch of coils moving down the slinky.
2
Water Ripples
Slow Tapping
Ripples are far apart.
Fast Tapping
Ripples are close together.
The Discovery Rule
"Faster tapping = closer ripples"
The ripples get closer together as you tap faster because you are putting more waves into the same space.
3
Waves Meeting
The Meeting
Waves combine for a split second to make a larger peak.
Aftermath
Waves pass right through each other cleanly and continue on their way.
Wave Task Cards Key Wave Task Answer Key
Task Card Solutions & Teacher Guide
Teacher Resource
1. The Quick Shake
The frequency increases.
Note: Shaking faster means more waves in the same amount of time.
2. Space Silence
Sound needs a material (matter) to travel through.
Note: Space is empty, so there is nothing to carry the sound.
3. Wave Drawing
Drawing should show the crest (top) and trough (bottom) labeled.
4. Wave Length
The wavelength increases.
Note: If waves move faster but the timing stays the same, the waves will stretch out.
5. The Squish
Compression
This is where the wave is squeezed together.
6. Energy Flow
The energy moves across the pool.
Key Point: The water doesn't travel; only the energy travels through the water.
7. Wave Size
Amplitude.
Note: Pushing with more force makes the wave go higher or lower.
8. The Human Wave
Side-to-Side Wave.
Note: People move up and down, but the wave moves across the stadium seats.
Teacher Guide
Common Mistake
Students often think water moves all the way across the ocean. Use Card 6 to show that if matter moved with the wave, the ocean would empty and fill constantly. Matter stays in place while energy moves through it.
Speed vs. Energy
Shaking a slinky faster doesn't always make the wave move faster. The wave speed is actually determined by the material of the slinky itself.
Wave Task Cards Activity 1
The Quick Shake
You are shaking a Slinky faster and faster. What happens to the frequency of the waves you are making?
Concept: Frequency
2
Space Silence
If a giant explosion happens in space, why can't astronauts hear it? Think: What do waves need to travel through?
Concept: Material
3
Wave Drawing
Draw a side-to-side wave on your sheet. Label the top and the bottom.
Skill: Drawing
4
Wave Length
If the frequency stays the same but the wave speed increases, what happens to the wavelength?
Concept: Rules
5
The Squish
Look at a push-pull wave. What do we call the part where the coils are squeezed together?
Concept: Parts
6
Energy Flow
A wave passes through a pool. Does the water move all the way across, or does only the energy move across?
Concept: Movement
7
Wave Size
You push a Slinky further to the side with more force. Which wave part did you just change?
Concept: Size
8
The Human Wave
During a "stadium wave," fans stand up and sit down as the wave passes. Is this a side-to-side or push-pull wave?
Application
Wave Task Worksheet
Name:
Date:
Draw & Label Here
Wave Discovery Teacher Guide Wave Discovery Teacher Guide
Setup Guide // Wave Discovery Lab
Materials Needed
For Each Group:
1 Slinky (metal is best)
1 Flat tray with a little bit of water
Tape to mark the floor
Paper towels for water spills
Teaching Tip
Turn the lights down and use a phone light above the water trays. The wave shadows on the table will look very clear, making it easier for students to see the patterns.
How to Teach This Lab
Phase 1: Discovery (20 mins)
Don't teach the big science words yet. Let them explore first. Walk around and ask: "Does the water actually move across the tray, or is it just the wave?"
What to Look For
Speed vs. Distance:
Students should see that faster tapping makes ripples closer together.
Waves Crossing:
Students should see waves passing through each other instead of bouncing off.
Quick Fixes
Problem: Tangled Slinkys
Tell students to keep the Slinky on the floor. If they lift it up, it will tangle or overstretch.
Problem: Water Everywhere
Remind students that they only need a tiny bit of water. Have paper towels ready at every station!
Wave Word Posters Activity Wave Word Posters
Vocabulary Poster Activity
Name:
Your Goal
Make a large Poster for one wave word. Your poster should help other students understand exactly how that part of a wave works.
1. Pick One Word
Side-to-Side Wave
Energy moves up and down
Push-Pull Wave
Energy moves by squishing
Frequency
How fast the wave moves
Wavelength
The length of one full wave
Amplitude
How high the wave goes
Interference
When two waves meet
2. Poster Checklist
Draw It
Draw the wave and label all its parts (like top, bottom, or the squished parts).
Explain It
Explain your word using an example from real life (like a heartbeat or a stadium wave).
Label It
Include the unit we use to measure it (like Hertz or meters) and a wave rule from our lab.
3. Practice Area
Sketch your poster layout here before you start the big one!
How You Will Be Graded
Word is big and easy to see
Drawing is neat and colorful
Definition is in your own words
Example is creative and makes sense
Wave Parts Cards Activity Wave Parts Cards
Sorting Wave Facts and Examples
Name:
Date:
Instructions: Cut out the cards below. Sort them into two piles: Side-to-Side waves or Push-Pull waves. If a card applies to BOTH , put it in the middle.
Right-Angle Motion
The wave moves forward while the particles move up and down.
Crest (Top)
The highest point of a wave.
Ocean Wave
A classic example of a side-to-side wave.
Parallel Motion
The wave and the particles move in the same direction.
Compression (Squish)
Where the particles are pushed close together.
Sound Wave
Energy moving through air by pushing particles.
Side-to-Side Slinky
Moving your hand left and right.
Push-Pull Slinky
Moving your hand forward and back.
Trough (Bottom)
The lowest point of a wave.
Material
The thing a wave travels through (like water or air).
Energy
What waves carry (they do NOT carry the material itself).
Amplitude (Height)
How big the wave is from its rest position.
Wavelength
Distance from one full cycle to the next.
Rarefaction (Stretch)
Where the particles are spread far apart.
Your Own Card
Add another wave fact or example here!
Answer Key
Wave Parts Card Sort
Side-to-Side
Right-Angle Motion
Crest (Top)
Trough (Bottom)
Ocean Wave
Side-to-Side Slinky
Push-Pull
Parallel Motion
Compression (Squish)
Rarefaction (Stretch)
Sound Wave
Push-Pull Slinky
Both (Universal)
These apply to all moving waves.
Material
Energy
Amplitude
Wavelength
Sound Properties Key Teacher Resource
Sound Properties Key
Sound Properties Lab Facilitation
Unit: Wave Runners
Answer Key
Setup Requirements
• 3 different tuning forks / rubber bands
• Bowls with tightly stretched plastic wrap
• Salt, sand, or rice for visualization
• Mallets or hands for striking forks
Pedagogical Tips
Remind students: Strike forks against palm/knee, NOT the table. Station 2 requires a "drum-tight" surface for the salt to dance.
Station 1: Pitch & Frequency
Log: Smallest = High pitch; Largest = Low pitch.
Analysis: Smaller objects vibrate faster. Higher frequency = Higher Pitch.
Station 2: Loudness & Amplitude
Observation: Hard strike = salt jumps higher; Soft strike = minimal movement.
Analysis: Loudness is Amplitude. More energy = Larger Amplitude (displacement).
Station 3: Medium & Speed
Observation: Sound is much louder/clearer through the table than through the air.
Diagnostic: Solids are denser; particles are closer, passing the energy more efficiently.
Final Inspection Synthesis
Engine speeds up → Frequency Increases. Since speed is constant in air, the Wavelength Decreases to compensate. This is an Inverse Relationship.
Misconception: Pitch = Volume. (Correct: Pitch = Frequency, Volume = Amplitude).
MS-PS4-1 | Sound Properties Key
Wave Properties Quiz Document Wave Properties Quiz
QUIZ-WAVE-02 • Wave Runners
Student Name
Date
Choose the best answer based on the PhET "Waves on a String" lab investigation.
How does Amplitude affect Wave Speed in the simulation?
Increasing amplitude significantly increases the wave speed.
Increasing amplitude decreases the wave speed.
Changing the amplitude has no significant effect on wave speed.
Wave speed is only affected by amplitude when damping is high.
Which variable directly alters the speed of the pulse through the medium?
Damping Level
Tension Level
Pulse Width Duration
Initial Amplitude
If you decrease Pulse Width at constant tension, what happens to Wavelength ?
The wavelength increases.
The wavelength decreases.
The wavelength remains exactly the same.
The wavelength becomes infinite.
What does the "No End" setting signify about the wave's environment?
The wave reflects once it hits the edge of the screen.
The wave travels out a window, preventing reflection/interference.
The tension is so high that the wave cannot reach the end.
The string is broken at one end, making the wave stop.
How does Low Tension wave speed compare to High Tension wave speed?
The speed is much faster at Low tension.
The speed is much slower at Low tension.
The speed is exactly the same at both tension levels.
The speed cannot be measured at Low tension.
Wave Runners Series • PHY-QUIZ-02
Superposition Intel Quiz Document Superposition Intel
Video Analysis Report: Professor Dave Series
Mission: Wave Interference
Name:
Date:
I. Superposition Foundations
1. Why can two mechanical waves occupy the same space at the same time, but two solid people cannot?
2. What is the technical term for the combination of two waves overlapping in the same space?
II. The Interference Spectrum
Constructive Interference
Occurs when amplitudes are added together to produce a larger wave.
Scenario Check:
When two crests align, what happens to the resultant amplitude?
Destructive Interference
Occurs when the resultant wave has a smaller amplitude than the individual waves.
Scenario Check:
If a resultant wave has an amplitude of zero, what is it called?
3. After two wave pulses finish interfering and continue moving, do they maintain their original characteristics or are they permanently changed?
4. Explain the difference between waves that are "exactly in phase" vs. "exactly out of phase."
III. Boundaries & Tech
How do noise cancellation headphones utilize the concept of "out of phase" signals to provide a quieter experience?
Boundary: Free to Move
A wave hits a boundary that is loose or movable.
Resulting Behavior:
Boundary: Fixed Point
A wave hits a wall or a boundary that is completely solid.
Resulting Behavior:
IV. Diffraction Phenomena
5. Define diffraction in your own words. What happens to a wave when it reaches a small gap?
6. The video mentions that a diffraction pattern is actually just another kind of interference pattern. Why is this? (Hint: Think about maxima and minima).
End of Intel Report // Secure Field Data // Wave Runner Tech Division
Wave Crossings Key CROSSINGS KEY
Venn Diagram Solution & Logic
Module W-CROSS-KEY
Correct Term Placement
Transverse Only
Crests & Troughs
Perpendicular
Light Waves
Seismic S-Waves
Both (Overlap)
Transfers Energy
Frequency
Wavelength
Amplitude
Oscillates
Reflects/Refracts
Longitudinal Only
Compressions
Rarefactions
Parallel
Sound Waves
Seismic P-Waves
Requires Medium
Technical Brief: Seismic Logic
Explanation: Longitudinal waves (P-waves) are compressional. In the Earth's crust (solids), the material resists compression more strongly than it resists "shear" or side-to-side motion (S-waves). Because the "restoring force" for compression is greater, P-waves travel significantly faster than S-waves. This is why seismographs always record the "Primary" compressional wave first, then the "Secondary" transverse wave.
Pedagogical Tip
Use the "Human Wave" analogy. Have students stand in a line. A longitudinal wave is a "shove" forward (parallel), while a transverse wave is a "stadium wave" with hands going up/down (perpendicular).
Common Misconception
Students often think all mechanical waves are longitudinal. Remind them that water waves are a complex transverse/longitudinal mix, and seismic S-waves are purely transverse mechanical waves.
Teacher Resource // Wave Runner Series
Answer Key
Wave Video Quiz Key Video Quiz Answer Key
Video: Wave Motion by FuseSchool
Teacher Key
Question 1
What do all waves move?
B) ENERGY
Question 2
Do people move seats?
No
Only energy travels; the matter stays in place.
Question 3
Through a vacuum?
Yes
Mechanical waves like sound cannot, but waves in general (like light) can.
Frequency Unit
HERTZ (Hz)
How often a cycle happens in one second.
Question 4
Time for one wave:
PERIOD
Measured in seconds.
Question 5
Symbol for wavelength:
Lambda
(λ)
Questions 6 & 7
What is amplitude?
Center line to the peak.
Flat Sea height:
Amplitude
Teacher Guide
Use this quiz as a quick check for understanding. The video covers core terminology needed for the Moving Waves Lab. Remember that while energy moves, the particles (people in seats) simply return to their original spot.
Teacher Guide // Video series 01
Internal Use Only
Harmonic Tension Mastery Pack Activity Acoustic Resonance
Technical Brief // String Tension Dynamics
Unit: Wave Runners
Technician Name
Calibration Date
The Physics of Tension
Standing waves occur when a wave interferes with its own reflection. For a string fixed at both ends, this creates regions of zero displacement (Nodes) and maximum vibration (Antinodes) .
The behavior is dictated by Tension (T) and Inertia (µ) . Tension provides the restoring force, while linear mass density (µ) represents the resistance to being moved.
The Velocity Law
The velocity (v) of a wave on a string is determined by the ratio of Tension to Density.
v = √(T / µ)
Variable µ (Mu)
Measured in kg/m. This tells us how "heavy" each meter of string is. High density strings require more force to move.
Harmonic Resonance
Strings naturally vibrate at a fundamental frequency (f1). Higher modes (fn) are simple whole-number multiples.
fn = n · f1
Visualizing Harmonics
1
Fundamental Mode
λ = 2L
2
2nd Harmonic
λ = L
Mode n = 1 Mode n = 2
Mission: 01
Technical Analysis
A string of length L = 1.40 m is stretched by a 2.00 kg mass. The string linear density is µ = 0.004 kg/m.
1. Setup Schematic
2. Variable Log
Mass (m)
Density (µ)
Length (L)
Gravity (g)
9.8 m/s²
3. Tension (T)
T = m · g
4. Speed (v)
v = √(T / µ)
5. Freq (f1)
f1 = v / (2L)
Theoretical Review
1. If hanging mass increases by 4x, the wave speed doubles. Why? Support your answer using v = √(T/µ).
Engineering Challenge: Why choose high density for deep notes?
Sonar Scouts Worksheet Sonar Scouts Worksheet
Depth Detection Challenge
Name:
Date:
Essential Formulas
\( v = \frac{d_{\text{total}}}{t} \)
Wave Speed
\( v = f \cdot \lambda \)
Wavelength
Sonar Pulse Tip
Sonar is a "round-trip" wave. The total distance is always twice the depth . Remember to convert milliseconds (ms) to seconds (s) by dividing by 1,000!
1 Mission: Calibration Test
Scaffolded Data
Depth is 50 m. Frequency is 50.0 kHz. Return time is 66.5 ms.
Nav Logic: We use the known depth to find the speed of sound in the specific water conditions of this area.
50m
A Total Distance (\(d_{\text{total}}\)):
B Time in Seconds (\(t\)):
C Sound Speed (\(v\)):
D Wavelength (\(\lambda\)):
2 Mission: Deep Trench Scan
Scaffolded Logic
Pulse is 30.0 kHz. Return time is 2.0 s. Speed is 1,500 m/s.
Nav Logic: We use sound speed and time to find the total distance, then divide by 2 to find the depth (one-way distance).
A Total Dist (\(v \times t\)):
B Ocean Depth (\(d / 2\)):
C Wavelength (\(v / f\)):
3 Mission: Submarine Stealth Mode
Scaffolded Data
Pulse is 120.0 kHz. Seafloor is 25 m below. Return time is 33.0 ms.
Nav Logic: High frequencies are used for short distances to get better resolution (accuracy) in shallow water.
A Total Dist (\(d \times 2\)):
B Time in Seconds (\(t\)):
C Sound Speed (\(v\)):
D Wavelength (\(\lambda\)):
4 Mission: Whale Navigation Echo
Scaffolded Data
Click is 150.0 kHz. Rock is 12 m away. Speed is 1,480 m/s.
Nav Logic: We use speed and distance to find out how long the whale has to wait for its "mental map" to update.
A Total Dist (\(d \times 2\)):
B Echo Time (\(d / v\)):
C Time in Milliseconds:
D Wavelength (\(\lambda\)):
Sonar & Wave Properties (f, \(\lambda\), v)
Sonar Scouts | Unit: Wave Runners
String Wave Lab Key Lab Report Key
Teacher Guide: PhET String Wave Investigation
ANSWER KEY
Expected Data Trends
Investigation 1: Amplitude vs Speed
Students should observe that Wave Speed is independent of Amplitude . The time taken to travel 6cm should remain constant (approx. 0.95s at High tension) regardless of whether amplitude is 1.00cm or 0.25cm.
Investigation 2: Pulse Width vs Wavelength
Students should observe an inverse relationship . As Pulse Width (which correlates to the period) decreases, the Wavelength (λ) also decreases.
Reasoning: Since v is constant, λ = v × pulse_width.
Investigation 3: Tension vs Speed
Students should observe that Tension directly controls Wave Speed .
High Tension: ~6.2 cm/s (Fastest)
Med Tension: ~3.8 cm/s
Low Tension: ~0.8 cm/s (Slowest)
Analysis Solutions
1. Amplitude & Speed
Answer: No. Amplitude does not affect speed.Evidence: The recorded times for 6.0 cm in Investigation 1 should be identical (within human error) for all three amplitude settings.
2. Tension & Speed
Answer: Tension has a direct positive relationship with speed.Rationale: Higher tension increases the restorative forces between the string particles, allowing the disturbance to propagate more rapidly through the medium.
3. Limits of the Model
Answer: The model assumes an ideal medium. By setting Damping to "None," students are removing air resistance and internal friction, which would normally cause the wave to lose amplitude (energy) as it travels. It also ignores gravitational effects on the string mass.
Wave Runners Series © 2026 • Lab Key 02
Superposition Intel Quiz Key Teacher Intel Key
Video Quiz: Interference & Diffraction
Internal Use Only
Pedagogical Resource
Superposition & Interference
1. Why can waves overlap while matter cannot?
Waves are not matter; they are displacements of matter that carry energy. Because they are energy disturbances, they can occupy the same space simultaneously, whereas matter (like solid people) is excluded from doing so.
2. Combined wave term?
Superposition (The resulting combined wave is called a superposition or resultant wave).
3. Wave characteristics after interference?
Waves maintain their own characteristics (amplitude, wavelength, velocity) after they pass through each other. Interference is a temporary state of overlapping, not a permanent change to the wave pulses.
4. In Phase vs. Out of Phase?
Exactly In Phase: Crests align with crests and troughs with troughs (constructive).Exactly Out of Phase: Crests of one align with the troughs of the other (destructive).
Tech & Boundaries
Noise Cancellation Mechanism:
Microphones detect background noise and generate a signal that is exactly out of phase (shifted by half a wavelength) with the noise. This creates complete destructive interference , canceling the sound waves before they reach the eardrum.
Free Boundary:
Wave reflects and bounces back in the opposite direction while maintaining the same amplitude (not inverted).
Fixed Boundary:
Wave reflects and is inverted (amplitude sign is flipped) as it bounces back.
Diffraction Phenomena
5. Diffraction Definition:
Diffraction is the bending of waves around edges or through small openings/gaps.
6. Why is it an interference pattern?
The "maxima and minima" (bright/dark or loud/quiet spots) result from the waves interfering with themselves as they bend and spread out from the opening, causing regions of reinforcement (constructive) and cancellation (destructive).
Video Transcript: Professor Dave Explains
Key ID: SUP-INTEL-KEY-V1
Acoustic Architecture Reading ACOUSTIC ARCHITECTURE
Background Reading: The Physics of Quiet
The Superposition Principle
In the physical world, two objects cannot occupy the same space. However, waves are not objects —they are disturbances. This property allows multiple waves to pass through the same point simultaneously. They obey the Principle of Superposition : the resulting displacement is the sum of the individual waves.
Imagine two ripples meeting. If two crests meet, they create a "super-crest." If a crest meets a trough, they flatten each other out. This interaction is called Interference .
Destructive Interference: The Shield
A "Sound Shield" occurs through Destructive Interference . This happens when waves are 180° "out of phase." The compression (high pressure) of one wave arrives at the exact moment as the rarefaction (low pressure) of another, effectively canceling the pressure change.
High Pressure + Low Pressure = Equilibrium (Silence)
Glossary
Phase The relative position of two waves in their cycle.
Path Length (d) The distance a wave travels from source to listener.
Node A point of zero amplitude caused by cancellation.
Mathematical Rule
Cancellation requires a path length difference (Δd) of exactly half a wavelength (λ/2).
Δd = λ / 2
Active Noise Control (ANC)
Noise-canceling headphones are a direct application of this theory. A microphone "listens" to ambient noise. A computer then plays the exact inverse wave (shifted by 180°). Because the speaker is mere millimeters from your ear, the two waves meet at your eardrum and destroy each other, leaving only the music you actually want to hear.
The ANC Feedback Loop
Engineer Review
Check for Understanding
1. Waves vs. Matter:
Why can two sound waves exist in the same spot, but two bricks cannot?
2. Dynamic Movement:
If you move a speaker 10cm further away from a "Quiet Zone," what happens to the volume? Why?
3. Technology Constraints:
Why do noise-canceling headphones struggle more with sudden loud shouts than with a steady airplane engine drone?
Wave Runner: Acoustic Engineering Division
Background Read 09-02
Superposition MCQ Quiz Document Superposition MCQ Intel
Video Assessment: Professor Dave Interference & Diffraction
Security Clearance: Level 1
Operator:
Date:
Select the most accurate technical response for each wave phenomenon described in the briefing. Ensure all data is logged correctly.
1. According to the principle of superposition, what happens when two mechanical waves occupy the same space?
They bounce off each other like solid objects
They combine to form a new pattern through addition
The higher energy wave destroys the lower energy wave
They stop moving and transfer all energy to the medium
2. What occurs immediately after two waves finish overlapping during interference?
They maintain their original characteristics and trajectories
They permanently merge into a single, larger wave pulse
They lose 50% of their amplitude due to energy friction
They reverse direction and return to their source origin
3. Which scenario results in "constructive interference"?
A crest of one wave aligns with a trough of another
Two waves move in opposite directions without meeting
The crests of two waves precisely align with each other
A wave hits a fixed boundary and becomes inverted
4. How do noise-canceling headphones achieve "complete destructive interference"?
By emitting a signal that is exactly in phase with noise
By physically blocking all air particles from entering the ear
By emitting a signal exactly 180 degrees out of phase
By increasing the frequency of noise until it is ultrasound
5. What happens when a wave reaches a fixed (immovable) boundary?
It is absorbed completely by the boundary material
It is reflected back with the same amplitude sign
It is reflected back and inverted (flipped)
It speeds up as it transitions into the new medium
6. Which phenomenon describes a wave bending around the edges of an opening?
Refraction
Diffraction
Polarization
Acceleration
7. Why is a diffraction pattern considered a type of interference pattern?
Because it only occurs when two different media collide
Because it generates a series of maxima and minima
Because it requires exactly three wave sources to form
Because it violates the superposition principle
Final Data Verification
Correct Logs:
Sonar Scouts Key Teacher Resource
Sonar Scouts Key
Solution Guide & Pedagogical Rationales
Unit: Wave Runners
Answer Key
1. Mission: Calibration Concept: v = d/t calibration
A) Distance: \( 50 \times 2 = \mathbf{100 \text{ m}} \)
B) Time: \( 66.5 \text{ ms} = \mathbf{0.0665 \text{ s}} \)
C) Speed: \( 100 / 0.0665 \approx \mathbf{1504 \text{ m/s}} \)
D) Wavelength: \( 1504 / 50,000 = \mathbf{0.03 \text{ m}} \)
Rationale: Calibrating with known depth is a real-world task. It forces students to handle the "double-distance" of echoes and "ms to s" conversion early.
2. Deep Trench Scan Concept: Solving for Distance
A) Total Dist: \( 1500 \times 2.0 = \mathbf{3000 \text{ m}} \)
B) Depth: \( 3000 / 2 = \mathbf{1,500 \text{ m}} \)
C) Wavelength: \( 1500 / 30,000 = \mathbf{0.05 \text{ m}} \)
Rationale: Shifts the variable from speed to depth. Students must remember the echo principle in reverse: finding the total distance first, then the depth.
3. Submarine Stealth Mode Concept: High Frequency in Shallows
A) Total Dist: \( 25 \times 2 = \mathbf{50 \text{ m}} \)
B) Time: \( 33 \text{ ms} = \mathbf{0.033 \text{ s}} \)
C) Speed: \( 50 / 0.033 \approx \mathbf{1,515 \text{ m/s}} \)
D) Wavelength: \( 1515.15 / 120,000 \approx \mathbf{0.01 \text{ m}} \)
Rationale: Tests accuracy at high frequencies. Higher frequency = smaller wavelength, which allows for better detection of small obstacles like reefs.
4. Whale Navigation Echo Concept: Solving for Time
A) Total Dist: \( 12 \times 2 = \mathbf{24 \text{ m}} \)
B) Time (s): \( 24 / 1480 \approx \mathbf{0.0162 \text{ s}} \)
C) Time (ms): \( 0.0162 \times 1000 \approx \mathbf{16.2 \text{ ms}} \)
D) Wavelength: \( 1480 / 150,000 \approx \mathbf{0.01 \text{ m}} \)
Rationale: The most complex algebra (solving for denominator). Students see biological echolocation in action with ultra-high frequencies.
Pedagogical Synthesis
• Cumulative Scaffolding: Each problem adds a layer (algebra, unit conversion, biological context) while reinforcing the core echo concept.
Wave Properties Quiz Key Quiz Answer Key
Teacher Resource: Wave Properties Check
QUIZ KEY
Correct Answers
1
Effect of Amplitude on Speed
Changing the amplitude has no significant effect on wave speed.
Rationale: Wave speed is a property of the medium. Changing the "push" (amplitude) only changes the energy carried, not how fast the medium responds.
2
Medium Property affecting Speed
Tension Level
Rationale: Tension changes the restorative force in the string. Higher tension allows the medium to snap back faster, speeding up propagation.
3
Pulse Width vs Wavelength
The wavelength decreases.
Rationale: Speed is constant. Because wavelength = speed × pulse_width, a shorter pulse width results in a physically shorter wave on the string.
4
No End Behavior
The wave travels out a window, preventing reflection and interference.
Rationale: This setting simulates an infinite string where the boundary doesn't exist, allowing for observation of single, non-interfering pulses.
5
Tension Comparison
The speed is much slower at Low tension.
Rationale: Low tension means less restorative force, making the "pulse" take longer to pull the next particle in the string, slowing the wave.
Wave Runners Series © 2026 • Quiz Key 02
Acoustic Architecture Key ARCHITECTURE KEY
Background Reading Solutions & Pedagogy
Module 09-02-KEY
Instructional Goal
Bridges mechanical wave properties (Slinkys) to acoustic engineering. Goal: view sound as a manipulatable pressure wave.
Misconception Alert
"Canceling" sound doesn't destroy energy; it redistributes it to areas of constructive interference (Antinodes).
Engineer Review Solutions
1. Waves vs. Matter
Expected Answer: Bricks are physical matter that take up space; waves are disturbances or energy moving through matter. Because waves are not physical objects, they can occupy the same coordinates without colliding, instead adding their energies together (superposition).
2. Dynamic Movement
Expected Answer: The volume will Increase . The "Quiet Zone" depends on a specific path length difference (λ/2). Moving the speaker changes that difference, pushing the waves out of their perfectly canceling alignment and allowing constructive or partial interference to occur.
3. Tech Constraints
Expected Answer: Steady sounds (like engines) are predictable; the computer can easily match the phase. Sudden shouts are unpredictable. The computer must detect the sound and calculate the inverse wave; if the sound is too fast, the cancellation wave arrives late, missing the target noise.
Design Challenge
Model Idea: Install external speakers on windows playing the "anti-noise" of construction equipment. Or, design "active curtains" that vibrate in the opposite direction of incoming street sounds to cancel them at the barrier.
Teacher Resource // Wave Runner Series
ANSWER KEY
Superposition MCQ Quiz Key MCQ Intel Master Key
Video Quiz: Interference & Diffraction
Internal Use Only
REFERENCE DATA
1. Principle of Superposition B
Waves are displacements of energy, not matter, allowing them to occupy the same space and combine through simple addition.
2. Post-Interference Behavior A
Waves are temporary disturbances. Once they pass through each other, they revert to their original shape, speed, and direction.
3. Constructive Interference C
Constructive interference requires the crests to line up (in phase), which results in a larger combined amplitude.
4. Noise-Canceling Tech C
By producing a sound wave that is shifted by half a wavelength (180°), the device creates destructive interference that cancels the ambient noise.
5. Fixed Boundaries C
When a wave pulse hits a fixed point, the third law of motion results in a reaction force that flips the pulse over (inversion).
6. Wave Bending B
Diffraction specifically refers to the bending of waves around obstacles or through narrow gaps.
7. Diffraction Pattern Nature B
A diffraction pattern is an interference pattern because it consists of areas of reinforcement (maxima) and cancellation (minima) as the wave bends.
Pedagogical Pointer:
Use this MCQ version for a quicker "check for understanding" or exit ticket. For a deeper dive into the science, use the "Intel Report" (FRQ version) which requires students to explain the "why" behind the behaviors.
Operator Key // Professor Dave Briefing // Wave Runner Intelligence
Wave Blueprint Worksheet Wave Blueprint Worksheet
Sound Wave Modeling & Math
Name:
Date:
The Wave Function Blueprint
\( y(x,t) = A \sin(kx - \omega t) \)
\( A = \text{Amplitude} \)
\( \lambda = v / f \)
\( k = 2\pi / \lambda \)
\( \omega = 2\pi f \)
1 Guided Build: Standard Speaker Tone
Round to Nearest Tenth
A speaker creates a tone at 261.6 Hz. The cone has a max displacement (A) of 0.60 cm. The speed of sound is 343 m/s.
A = 0.6 cm
Step A: Calculate Wavelength \( (\lambda = v/f) \)
meters
Step B: Find Wave Number \( (k = 2\pi/\lambda) \)
rad/m
Step C: Find Angular Frequency \( (\omega = 2\pi f) \)
rad/s
Construct Final Representation \( y = A \sin(kx - \omega t) \)
2
System Mod: The Subwoofer Drop
Input: 40 Hz | 2.5 cm | 343 m/s
Calculations \( (\lambda, k, \omega) \):
Final Representation:
3
System Mod: The Underwater Pinger
Input: 1,000 Hz | 0.1 cm | 1,500 m/s
Calculations \( (\lambda, k, \omega) \):
Final Representation:
Modeling Waves (f, \( \lambda \), v, k, \( \omega \))
MS-PS4-1 | Wave Runner Series
Wave Blueprint Key Teacher Resource
Wave Blueprint Key
Mathematical Modeling Solution Guide
Unit: Wave Runners
Answer Key
1. Guided Build: Standard Speaker Tone v = 343 | f = 261.6 | A = 0.6
Step A (\(\lambda\)): \( 343 / 261.6 \approx \mathbf{1.3 \text{ m}} \)
Step B (\(k\)): \( 2\pi / 1.311 \approx \mathbf{4.8 \text{ m}^{-1}} \)
Step C (\(\omega\)): \( 2\pi \times 261.6 \approx \mathbf{1643.7 \text{ s}^{-1}} \)
Model:
\( y(x,t) = 0.6 \sin(4.8x - 1643.7t) \)
2. The Subwoofer Drop v = 343 | f = 40.0 | A = 2.5
Step A (\(\lambda\)): \( 343 / 40.0 = \mathbf{8.6 \text{ m}} \)
Step B (\(k\)): \( 2\pi / 8.575 \approx \mathbf{0.7 \text{ m}^{-1}} \)
Step C (\(\omega\)): \( 2\pi \times 40.0 \approx \mathbf{251.3 \text{ s}^{-1}} \)
Model:
\( y(x,t) = 2.5 \sin(0.7x - 251.3t) \)
3. The Underwater Pinger v = 1500 | f = 1000 | A = 0.1
Step A (\(\lambda\)): \( 1500 / 1000 = \mathbf{1.5 \text{ m}} \)
Step B (\(k\)): \( 2\pi / 1.5 \approx \mathbf{4.2 \text{ m}^{-1}} \)
Step C (\(\omega\)): \( 2\pi \times 1000 \approx \mathbf{6283.2 \text{ s}^{-1}} \)
Model:
\( y(x,t) = 0.1 \sin(4.2x - 6283.2t) \)
Pedagogical Synthesis
• Unit Management: Keep Amplitude in cm for displacement visibility, but ensure \(k\) is in m-1 for meters.
• Angular vs Cyclic: Note the \(2\pi\) factor required by the sine function's radian input for \(k\) and \(\omega\).
• Directionality: The minus sign in \((kx - \omega t)\) defines a wave traveling in the positive x-direction.
Wave Blueprint | Key
MS-PS4-1 | NGSS Physics
Optic Runners Slides Optic Runners
Light, Lenses, and the Geometry of Vision
Unit 3: Optics
Wave Physics
The Nature of Light
Wave Properties
Light behaves as a transverse wave. It can be reflected, refracted, and diffracted.
Evidence: Interference patterns
Particle Nature
Light also travels in discrete packets of energy called Photons.
Evidence: Photoelectric effect
We call this Wave-Particle Duality.
Mirror Magic
Concave
The "Cave" effect. Surface curves inward, causing rays to converge at a focal point.
Usage
Makeup mirrors, Telescopes
Convex
The "Exit" effect. Surface curves outward, causing rays to diverge away from each other.
Usage
Security mirrors, Car mirrors
The Mirror Lexicon
Principal Axis
The horizontal line passing through the center of the mirror or lens.
Vertex (V)
The point where the principal axis meets the mirror surface.
Center of Curvature (C)
The center of the sphere from which the mirror was cut.
Focal Point (F)
The point where parallel rays converge (or appear to diverge from).
Focal Length (f)
The distance from the vertex to the focal point. f = R / 2
Radius of Curvature (R)
The distance from the vertex to the center of curvature.
Mirror Geometry
Principal Axis C Center of Curvature F Focal Point V Vertex f R
Lens Logic
Converging
Thicker in the middle than at the edges. Also known as Convex Lenses.
Magnifies Images
Diverging
Thinner in the middle than at the edges. Also known as Concave Lenses.
Shrinks Images
The Lens Lexicon
Optical Center
The precise geometric center of the lens where rays pass through unbent.
Double Focal Length (2F)
A point twice the distance from the lens as the focal point.
Lens Power (P)
The ability of a lens to bend light. P = 1 / f (measured in Diopters).
Magnification (M)
The ratio of image height to object height. M = hi / ho.
Lens Geometry
Optical Center F 2F F 2F Focal Length (f)
Light Logic Lab Manual Light Logic Lab
Reflection & Refraction
Name: ____________________
Date: ____________________
The Secret Life of Rays
Light travels in straight lines called rays . When a ray hits a surface like a mirror, it performs a reflection . This bounce follows the Law of Reflection : the angle of incidence (incoming) equals the angle of reflection (outgoing).
When light enters a new material like water, it undergoes refraction . This change in speed causes the light to bend. In this lab, you will model these behaviors to see how light behaves at boundaries.
Materials Checklist
Plane Mirror & Support
Protractor Sheet
Corks & Pins
Semicircular Dish
Toothpick & Water
Safety Protocol
"Protect your optics!"
1. Bright Lights: Do not look directly at the sun or high-intensity light sources through lenses.
2. Spill Control: We are using water on paper. Wipe spills immediately to keep your measurements clear.
Part I: Reflection
Goal: Mapping the Law of Reflection
Place your mirror exactly along the 90° line in the center of the protractor sheet.
Place a cork at the 40° mark in Quadrant 4. This is your target .
Look from Quadrant 3. Align the reflection with the center crosshair. Record your eye's angle.
Place a pinned cork behind the mirror where the image appears to be.
Repeat with two new angles of your choice in Quadrant 4.
Normal Line (0°) Target (Q4) Eye (Q3)
Fig 1: Reflection Layout
Table 1: Reflection Data
Target (Object) Eye (Reflection) Virtual (Image) Quad Angle Quad --- --- --- 4 40° 4 ______ 4 ______
Snells Law Secret Key Snell's Law Secret
Teacher Answer Key
CODE: REFRACT-DERIVE-09-KEY
Confidential
Mission Summary: Students discover that light bending follows a linear proportionality between the sines of angles. The slope (\(n \approx 1.33\)) represents the index of refraction for water.
Step 1: Processed Data
Air (θi) Water (θr) sin θi sin θr Ratio 10° 7.5° 0.174 0.131 1.33 20° 14.9° 0.342 0.257 1.33 30° 22.1° 0.500 0.376 1.33 40° 28.9° 0.643 0.483 1.33 50° 35.2° 0.766 0.576 1.33
Step 2: Trends
Q1: Pattern
Ratios are constant (~1.33), showing proportionality.
Q2: Linearity
Plotting sines creates a linear model for refraction.
Optical Plot: Best Fit Line
sin θr (Refracted)
sin θi (Incidence)
0
0.50
1.0
0
0.50
1.0
Derivation
Slope (m):
1.33
Slope = n2 / n1
Note:
Data shows nwater = 1.33. This is consistent with established optical tables.
The Discovery
By plotting sines, students arrive at the governing law of optics.
n1 · sin(θ1) = n2 · sin(θ2)
Final Mathematical Model: Snell's Law
Ray Relay Lab Manual Ray Relay Lab
Phase 1: Reflection & Refraction Inquiry
Name: ________________
Date: ________________
Objective
Develop models to represent conditions that cause diffraction, reflection, or refraction of different wave types and collect precision data for Snell's Law.
Materials
• Plane Mirror & Support
• Semicircular Lens
• Protractor Sheet
• Laser Pointer/Ray Box
• Cork & Pins
• 100 mL Water
Safety
Never look directly into the laser beam or point it at others. Avoid reflections into eyes. Handle glass lenses with care to avoid breakage.
Task 1: The Mirror Bounce
Setup: Place the mirror surface along the baseline of your protractor sheet, centered on the intersection with the Normal Line.
Aim your light ray at the center of the mirror (the 0° point).
Measure the Angle of Incidence (θi) and the Angle of Reflection (θr) .
Repeat for 3 different angles.
Trial Angle of Incidence Angle of Reflection 1 30° 2 45° 3 60°
Workspace: Sketch Trial 2
Normal
Task 2: Into the Medium
Setup: Place the flat side of the semicircular lens along the horizontal baseline. Aim light through the center point.
Procedure:
Aim the laser from Air into the Lens at the specified angles.
Observe how the ray bends toward the Normal Line.
Record the refracted angle inside the glass.
Challenge: Aim through the curved side toward the center. Does it bend at the same point?
Prediction:
When light slows down entering a denser medium, it will bend:
Toward the normal
Away from the normal
Trial Incidence (Air) Refracted (Glass) Refracted (Water) 1 20° 2 40°
Optic Mastery Worksheet v2 Optic Mastery Challenge
Mission: Comprehensive Unit Assessment
Name:
Date:
1 The Optic Lexicon
Center of Curvature
Optical Center
Principal Axis
Focal Length
Magnification
Vertex
A. Distance from Vertex to F.
B. Point where Axis meets Mirror.
C. Center of the Sphere.
D. Ratio of hi to ho.
E. Geometric center of a Lens.
F. Main line through the center.
2 The Artifact ID
A. Rays pass through and meet at a point on the opposite side.
B. Rays reflect and spread out; image is virtual & diminished.
C. Rays pass through and spread out, appearing to come from F.
D. Rays reflect and converge in front of the surface.
3 The Ray Detective
Orientation
Upright Inverted
Type
Real Virtual
Size
Diminished Magnified
4 Snell's Calculation
A laser enters crystal from air (n=1.00). Incident angle = 45°; Refracted angle = 28°. Calculate the index n.
Solve Below:
n = ________
5 Biological Optics
1. Why is the image on the retina considered Real?
2. Explain why Myopia requires a Diverging lens.
6 Data Trends
If the slope of the sin θi vs sin θr graph increases, what does that tell you about the speed of light in the second medium?
End of Mission. Review for accuracy.
Light Logic Lab Key Teacher Key
Light Logic Key
Reflection & Refraction
Optic Runners
Reading Summary
"Light travels in straight rays and performs reflection (bouncing) or refraction (bending at boundaries). The Law of Reflection states Angle of Incidence = Angle of Reflection. Refraction occurs due to speed changes between media."
Table 1: Reflection Model Data
Incident (Q4) Reflection (Q3) Virtual (Q1) Angle 40° Angle 40° Angle 40° Angle 60° Angle 60° Angle 60°
1. The Bounce Trend
Answer: Angle of Incidence = Angle of Reflection. Light bounces off the surface at the same angle it entered, relative to the normal.
2. The Virtual Shadow
Answer: The image is the same size as the object and appears at the same distance behind the mirror as the object is in front.
Refraction Solutions
Air → Water (Slows Down)
Incid. Refr. 50° ~35° 30° ~22° 70° ~45°
Trend: Bends TOWARD normal
Water → Air (Speeds Up)
Incid. Refr. 45° ~70° 30° ~42° 10° ~13°
Trend: Bends AWAY from normal
1 The Classroom Mirror
Answer: Student 5. Due to the Law of Reflection (\(\theta_i = \theta_r\)), light rays from Student 5 hit the mirror at an angle and bounce to Student 1.
2 The Archer Fish Puzzle
Answer: BELOW. Light from the insect refracts as it enters the water, bending toward the fish's normal. This makes the insect appear higher in the air than it truly is.
Wave Runners Sequence Confidential Key
Optic Mastery Key Optic Mastery Master Key
Teacher Resource / Confidential
Mission 1: The Optic Lexicon
Center of Curvature: C
Optical Center: E
Principal Axis: F
Focal Length: A
Magnification: D
Vertex: B
Mission 2: The Artifact ID
A: Converging Lens
B: Convex Mirror
C: Diverging Lens
D: Concave Mirror
Mission 3: Ray Diagram
Inverted
Real
Diminished
Mission 4: Snell's Law Solution
Formula: n1 sin(θ1) = n2 sin(θ2)
Substitution: (1.00) sin(45°) = n2 sin(28°)
Calculate: 0.707 = n2 (0.469)
Solve: n2 = 1.51 (Crown Glass)
Mission 5: Biological Key
Q1 Real Image: Light rays physically converge at the retina surface. Can be displayed on a surface.
Q2 Myopia Fix: Diverging lens spreads rays out before they enter the eye, moving the early focal point back to the retina.
Mission 6: Data Trends Key
Slope = n2/n1.
If slope increases, n2 is higher.
Higher index of refraction means the speed of light in the second medium has DECREASED.
Snells Law Secret Worksheet Snell's Law Secret
Mathematical Modeling of Hooke's Refraction
CODE: REFRACT-DERIVE-09
Student Data Sheet
The Mission
Centuries ago, Robert Hooke observed how light bent when passing from air into water. He recorded the angles, but he didn't have the equation we use today. Your goal is to analyze his "raw data" to discover the mathematical relationship between the Angle of Incidence and the Angle of Refraction .
Step 1: Process the Raw Data
Angle in Air (θi) Angle in Water (θr) sin θi sin θr Ratio: sin θi / sin θr 10° 7.5° 20° 14.9° 30° 22.1° 40° 28.9° 50° 35.2°
Step 2: The Trend Line
Q1: Pattern Recognition
Look at your ratios in the last column. What do you notice about the values as the angles increase?
Q2: Linearity Check
If you plotted θi vs θr, would the line be straight? Why do we plot sine values instead?
Optical Plot: sin θi vs sin θr
sin θr (Refracted)
sin θi (Incidence)
0
0.25
0.50
0.75
1.0
0
0.25
0.50
0.75
1.0
Plot your 5 points. Use a ruler to draw a best-fit line through the origin.
Step 3: Deriving the Law
The slope of your line represents the Index of Refraction (n) for water.
Calculate Slope (m):
m = Δsin θi / Δsin θr = ________
Final Mathematical Model:
n1 ⋅ sin(θ1) = n2 ⋅ _________
This relationship is known as Snell's Law.
Optic Runner Cornell Notes Optic Runner Notes
Name
Date
Topic: Unit 3 - Optics Foundations EQ: How does geometric optics define our perception?
Cues / Questions
Note-Taking Area
Nature of Light
Duality
Wave Evidence:
Particle Evidence:
Mirror Lexicon
Geometric Terms
Vertex:
Center of Curv:
Principal Axis:
Focal Length:
Lens Lexicon
Refraction Terms
Optical Center:
Lens Power:
2F Point:
Magnification:
Image Lexicon
Appearance
Upright:
Inverted:
Magnified:
Diminished:
Optic Runner Notes • Part 2
Ray Anatomy
Standard Paths
1
Parallel Ray:
2
Central Ray:
3
Focal Ray:
Snell's Law
Bending Math
n1 sin(θ1) = n2 sin(θ2)
Defining Index of Refraction (n):
Optic Runner Notes • Part 3
The Human Eye
Biological Optics
Flexible Lens
Retina Sensor
Vision Fixes
Myopia & Hyperopia
Myopia: Corrected with lens.
Hyperopia: Corrected with lens.
Advanced Waves
Diffraction & Thin Film
Diffraction is bending around .
Thin film interference involves reflections off surfaces.
Mastery Summary
Explain how artifacts manipulate light geometry to correct or enhance human vision.
Optic Anatomy CER Packet Optic Anatomy
Biological Wave Control
Name: ________________
Date: ________________
The Living Lens
Refraction isn't just for prisms; it's a fundamental tool of survival. In animals, the evolution of the eye is a masterclass in wave control. The crystalline lens in your eye uses refraction to focus light onto the retina. By changing the shape of this lens (accommodation), your body adjusts its focal length, allowing you to see objects both near and far.
But some animals take it further. The Archerfish , for example, shoots jets of water at insects on low-hanging branches. Because of refraction, the bug's apparent position in the air is different from its actual position. The archerfish has evolved to mathematically compensate for this "optical shift," aiming its shot at the true position rather than the visual image.
Structural Color is another optical marvel. The vibrant, iridescent blues of the Morpho butterfly or the peacock's tail aren't made of blue pigment. Instead, microscopic scales on their wings or feathers are layered in a way that causes light to refract and interfere. Only specific wavelengths (like bright blue) are reflected back, while others are canceled out.
Finally, consider the selective pressure of vision. The ability to focus light through a lens provides a distinct survival advantage—catching prey and avoiding predators. This explains why complex eyes have evolved independently multiple times across the animal kingdom, a process called convergent evolution.
From the Video: Refraction in Animals
Identify two specific ways refraction affects animal biology as shown in the "Refraction in Animals" explain video:
Biological Effect 1:
Biological Effect 2:
Claim • Evidence • Reasoning
Prompt: Compare the behavior of waves in a liquid medium (like the archerfish's water) to the behavior of light. Based on your lab data and reading, is light a wave, a particle, or both? Support your claim using specific evidence from reflection and refraction.
The Claim
A concise statement answering the prompt.
The Evidence
Specific observations from your lab (angles, bending, speed changes) or text.
The Reasoning
Connect your evidence to the scientific principles (Snell's Law, Wave Properties).
Phase 2: Refraction Discussion Rubric
Self-Assessment & Peer Review Protocol
Instructions: 1. Review your own CER using the checklist. 2. Swap with a partner. 3. Circle criteria missed by your peer. 4. Meet in groups of 3 to discuss discrepancies and revise before final submission.
Optic Runner Notes Key Optic Runner Notes KEY
Teacher Resource • Lexicon Update
Nature of Light
Wave Evidence: Interference, Reflection, Refraction.
Particle Evidence: Photons, Photoelectric Effect.
Mirror Lexicon
Vertex: Point where axis meets mirror surface.
Center of Curv: Center of original sphere.
Principal Axis: Line through C and V.
Focal Length: f = R/2; distance from V to F.
Lens Lexicon
Optical Center: Center where rays don't bend.
Lens Power: 1/f; measured in Diopters.
2F Point: Twice the focal length.
Magnification: hi/ho ratio.
Image Lexicon
Upright: Same orientation.
Inverted: Upside down.
Magnified: Image > Object.
Diminished: Image < Object.
Optic Runner Notes KEY • Part 2
Ray Anatomy
1. Parallel: Exits through far focal point (F).
2. Central: Exits straight through center (no bend).
3. Focal: Enters through near focal point, exits Parallel.
Snell's Law
Index of Refraction (n):
Measure of optical density; indicates how much the medium slows down light speed.
Optic Runner Notes KEY • Part 3
Human Eye
Lens: Flexible converging lens to focus rays.
Retina: Sensor surface for real images.
Vision Fixes
Myopia: Fix with DIVERGING lens.
Hyperopia: Fix with CONVERGING lens.
Advanced Effects
Diffraction: Bending around CORNERS / SLITS.
Thin film: Reflections off TOP AND BOTTOM surfaces.
Ray Geometry Practice Set Ray Geometry
Independent Practice: Modeling Reflection & Refraction
Name: ________________
Date: ________________
Set 1
Lenses & Magnification
Problem 1.1: A student uses a convex magnifying glass to read fine print. The focal length (f) of the lens is 10 cm. If the lens is held 6 cm (do) from the text, where is the image formed (di)? Is it real or virtual?
Variables: f = 10cm | do = 6cm
Mathematical Derivation:
1 / f = 1 / do + 1 / di
Image Location:
di = _______
Ray Diagram Workspace
Lens F F
Draw the object at 6cm (inside F). Use a ruler to trace parallel and focal rays to find the virtual intersection.
Set 2
Snell's Law: Boundary Shifts
2.1 Index Discovery: Light travels from air (n1=1.00) into an unknown clear liquid at 45°. The refracted angle in the liquid is 32°. Calculate n2.
n1 sin θ1 = n2 sin θ2
n2 (Liquid) = ________
2.2 Optical Speed Check: Light travels from water (n=1.33) into glass (n=1.52). If light enters the glass at 30°, calculate the refracted angle (θ2).
θ2 (Glass) = ________
Set 3
Visual Shift: Apparent Depth
Mission: Drafting the Lie
Light reflecting off a submerged object must pass from High Density (Water) to Low Density (Air). According to Snell's Law, as light speeds up, it bends away from the normal .
Trace the rays to reveal the "Ghost Duck"
AIR (n=1.00) WATER (n=1.33) Actual Position
1. Draw ray from Duck to Surface
2. Trace refracted ray to the Eye
3. Project Eye-Ray back underwater
4. Mark the Apparent Duck
Analytical Review:
1. Does the submerged object appear deeper or shallower than its true location?
2. If you were an archerfish, where would you aim to hit the duck?
The "Why":
Explain why light bends away from the normal when moving from water to air using the relationship between wave speed and medium density.
Optic Data Skills Worksheet Optic Data Skills
Math Skills: Trend Lines & Correlation
Name: ________________
Date: ________________
Mission 1: The Best Fit Line
A line of best fit (or trend line) is a straight line that best represents the data on a scatter plot. It shows the overall direction of the relationship.
Optical Data Set: Refraction Index
Task: Draw one straight best-fit line through the center of the points.
Analysis Checklist:
Does your line go through the origin (0,0)? Why is this necessary for physical data like refraction?
Identify the RED outlier. How did you handle it when drawing your line?
Student Response Area:
Mission 2: Correlation Analysis
Match the physical relationship to the visual plot.
Plot Alpha
Plot Beta
Plot Gamma
Positive Correlation:
As X increases, Y increases. (Plot: ________)
Negative Correlation:
As X increases, Y decreases. (Plot: ________)
No Correlation:
Points are scattered randomly. (Plot: ________)
The Physics of Slope
In your Snell's Law lab, if you plot sin θi on the Y-axis and sin θr on the X-axis, the slope (m) is equal to the index of refraction (n).
Problem Scenario:
A line of best fit for light entering glass has data points at (0.4, 0.6) and (0.2, 0.3). Calculate the index of refraction.
Mathematical Solve:
m = ΔY / ΔX
n = __________
Optic Runner Quiz Document Optic Runner Quiz
Wave Optics & Light Properties
Name: ________________
Date: ________________
1. When a light wave travels from air into a diamond (a much denser medium), what happens to its speed and direction relative to the normal?
The light speeds up and bends away from the normal.
The light slows down and bends toward the normal.
The light slows down and bends away from the normal.
The light speeds up and bends toward the normal.
2. An archerfish sees a bug in the air while looking from underwater. Due to refraction, where does the bug appear to be compared to its actual position?
It appears lower and closer to the water surface than it actually is.
It appears higher and further from the water surface than it actually is.
It appears in the exact same spot; refraction only happens in glass.
It appears blurred because light cannot refract through a water-air boundary.
3. A convex mirror, like those used for security in store aisles, always produces what kind of image?
A real, inverted image that is larger than the object.
A virtual, upright image that is smaller than the object.
A real, upright image that is smaller than the object.
A virtual, inverted image that is larger than the object.
4. According to Snell's Law (n1 sin θ1 = n2 sin θ2), what does the value of "n" represent?
The total amount of energy reflected off the surface.
The ratio of the speed of light in a vacuum to its speed in a medium.
The wavelength of the light being used in the experiment.
The distance from the normal line to the point of incidence.
Part II: Mathematical Modeling
5. A light ray enters a glass block (n=1.5) from air (n=1.0) at an angle of 30°. Calculate the refracted angle. Show your work clearly.
Refracted Angle: ________
6. Draw a precision ray diagram showing light reflecting off a plane mirror. Label the Incidence Ray, Reflected Ray, Normal Line, and both angles (θi, θr).
Diagram Workspace
Optic Runner Master Key Optic Runner Key
Teacher Resource: Block 5-7 Master Guide
CONFIDENTIAL
Snell's Law & Data Skills
Hooke's Data Table:
sin(10°) / sin(7.5°) 0.174 / 0.131 = 1.33
sin(30°) / sin(22.1°) 0.500 / 0.376 = 1.33
sin(50°) / sin(35.2°) 0.766 / 0.576 = 1.33
Teacher Note: Ratios and Slope should match 1.33 (Index of Water).
Data Skill Mission 2:
Alpha: Negative Correlation
Beta: Positive Correlation
Gamma: No Correlation
Slope Calculation (n):
(0.6 - 0.3) / (0.4 - 0.2) = 0.3 / 0.2 = 1.5
Ray Geometry Mastery
Problem 1.1: Magnifying Glass
1/10 = 1/6 + 1/di → 1/di = 1/10 - 1/6 = (3-5)/30 = -2/30
Problem 2.1: Unknown Liquid
1.00 ⋅ sin(45°) = n2 ⋅ sin(32°) → 0.707 = n2 ⋅ 0.530
Rubber Duck Analysis:
Light travels from High Index (n=1.33) to Low Index (n=1.00).
Rationale: According to Snell's Law, when light speeds up crossing a boundary into air, the refracted ray must bend away from the normal . This shift makes the light appear to originate from a point closer to the surface.
Effect: Object appears shallower than actual depth.
Quiz Solutions
Q Correct Answer Scientific Rationale 1 Slows down / Toward normal Higher n (optical density) always results in lower wave velocity and a smaller refracted angle. 2 Higher and further Perspective: Above water looking at air. Light entering water from air (the bug's light) bends toward the normal, projecting the image higher. 3 Virtual, upright, smaller Convex surfaces diverge rays; the virtual intersection is always smaller and behind the mirror. 4 Ratio: speed in vacuum to medium Absolute index of refraction definition: n = c / v. 5 19.5° sinθ2 = (1.0 ⋅ sin 30) / 1.5 = 0.5 / 1.5 = 0.33 → arcsin(0.33) ≈ 19.5°
Optical Artifacts Sort Activity Optical Artifacts
Classification & Property Sort
Name: ________________
Date: ________________
Sorting Mission
Cut out the property cards below. Analyze the physical shape, light behavior, and image properties to correctly classify each optical artifact. Paste or write the descriptions into the Master Matrix on page 2.
Physical Shape
Perfectly flat, silvered surface
Physical Shape
Curved inward like a cavern entrance
Physical Shape
Curved outward like a polished sphere
Physical Shape
Thicker in the center than at the edges
Physical Shape
Thinner in the center than at the edges
Behavior
Reflection: Light bounces off at equal angles
Behavior
Converging: Focuses light to a point
Behavior
Diverging: Spreads light rays apart
Behavior
Converging: Focuses light to a point
Behavior
Diverging: Spreads light rays apart
Typical Image
Virtual, Upright, and Same Size
Typical Image
Real/Inverted OR Virtual/Magnified
Typical Image
Always Virtual, Upright, and Reduced
Typical Image
Real/Inverted OR Virtual/Magnified
Typical Image
Always Virtual, Upright, and Reduced
The Master Matrix
Artifact Physical Shape Light Behavior Typical Image Plane Mirror Concave Mirror Convex Mirror Convex Lens Concave Lens
Synthesis Observation:
Look at the "Behavior" column. Which two artifacts are converging ? Which two are diverging ? What do you notice about their typical image properties?
Optical Artifacts Key Optical Artifacts Key
Teacher Resource: Classification Master
CONFIDENTIAL
Sorting Solutions
Artifact Physical Shape Light Behavior Typical Image Plane Mirror Flat, silvered surface Reflection: Rays bounce at equal angles Virtual, Upright, Same-Size Concave Mirror Curved inward like a cavern Converging Real/Inverted or Virtual/Upright Convex Mirror Curved outward like a ball Diverging Virtual, Upright, Reduced Convex Lens Thicker in the center Converging Real/Inverted or Virtual/Upright Concave Lens Thinner in the center Diverging Virtual, Upright, Reduced
Guiding Questions
• Shape & Logic: "If the lens is 'caved in' at the center, does light have more or less material to travel through?"
• Security Mirrors: "Why do stores use convex mirrors instead of plane mirrors? (Field of view context)"
• Real vs. Virtual: "Can you project a virtual image onto a screen? Why not?"
Common Errors
• Mixing Terms: Students often swap Concave Mirror (converging) and Concave Lens (diverging). Remind them that mirrors reflect, lenses refract.
• Virtual Bias: Students may think all images are real. Emphasize that virtual images are where light rays appear to meet.
