Doppler effect for sound waves

When a source of sound moves relative to a stationary observer, the frequency of the sound heard by the observer is different from the frequency emitted by the source. This phenomenon is called the Doppler effect.

If the source moves towards the observer, the sound waves are compressed, resulting in a higher observed frequency (pitch). If the source moves away, the waves are stretched, and the observed frequency is lower.

The Doppler effect occurs because the motion of the source changes the spacing (wavelength) of the sound waves reaching the observer.

Formula for the observed frequency

When a source of sound moves at speed $v_s$ relative to stationary air (and observer), and the speed of sound in air is $v$, the observed frequency $f_o$ is given by:

Explanation of signs:

• Source moving towards observer: $v - v_s$ (frequency increases)
• Source moving away from observer: $v + v_s$ (frequency decreases)

Example calculation

Key points

• The Doppler effect explains changes in pitch of sirens or horns as vehicles pass by.
• The effect is only due to the motion of the source (for this syllabus section).
• The observed frequency increases as the source approaches and decreases as it moves away.