Lesson 02

PITCH
MATH

Mastering the general Doppler equation for moving sources and observers.

The Doppler Equation

\[ f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right) \]

\( f' \) Perceived Freq

\( f \) Source Freq

\( v \) Speed of Sound

\( v_o , v_s \) Velocities

Sign Conventions

The "TOP" rule for the signs (\(\pm\)):

APPROACHING

Anything moving TOWARD the other party causes an INCREASE in frequency.

Observer moves toward source: \( + v_o \)

Source moves toward observer: \( - v_s \)

RECEDING

Anything moving AWAY from the other party causes a DECREASE in frequency.

Observer moves away: \( - v_o \)

Source moves away: \( + v_s \)

Example: The Ambulance

An ambulance emits a siren at 400 Hz while driving toward a stationary observer at 35 m/s. If the speed of sound is 340 m/s, what frequency does the observer hear?

Givens

\( f = 400 \text{ Hz} \)
\( v = 340 \text{ m/s} \)
\( v_s = 35 \text{ m/s} \)
\( v_o = 0 \text{ m/s} \)

The Setup

\[ f' = 400 \left( \frac{340 + 0}{340 - 35} \right) \]

\( f' \approx 446 \text{ Hz} \)

Pitch Math

Doppler Math Slides

Pitch Shift Practice Worksheet

Equation Master Answer Key