7.3 Doppler effect for sound waves

When a sound source moves relative to an observer, wavefront spacing changes, so the observed frequency differs from the emitted frequency.

Approaching motion produces compressed wavefronts and higher observed frequency; receding motion produces greater spacing and lower frequency.

A passing siren sounds higher before it reaches you and lower after it passes, even though the siren emits a steady tone.

The Doppler shift is not caused by the source changing its intrinsic frequency; it is a relative-motion observation effect.

For a source moving relative to a stationary observer in a medium, f_o=f_s v/(v±v_s), using the sign that gives higher frequency for approach and lower for recession.

Define source speed and wave speed in the medium, then choose the sign from the physical motion rather than memorising it blindly.

An approaching siren produces compressed wavefronts, so f_o exceeds f_s; after passing, the denominator changes and the observed frequency falls.

The source speed is measured relative to the medium in this model, not automatically relative to the observer; the sign must match approach or recession.