The Doppler Effect and Beats

The Doppler effect describes how the perceived frequency of a wave changes when the source and the observer are in relative motion with respect to each other. You have surely heard it without knowing it: the sound of an ambulance seems higher-pitched as it approaches you, then becomes lower as soon as it moves away, even though the siren itself always emits the same frequency.

The explanation lies in the compression of the wavefronts. When the source moves toward the observer, each new wavefront is emitted a little closer to the previous one: the fronts pile up in front of the source, the perceived wavelength decreases, so the perceived frequency increases, since v = λ × f and v remains fixed by the medium. Conversely, behind the receding source, the wavefronts stretch out: the perceived wavelength increases, and the perceived frequency decreases.

This phenomenon has essential applications: traffic radars measure a vehicle's speed from the frequency shift of the reflected wave, and astronomy uses the Doppler shift of starlight to tell whether stars are moving away from or toward us, revealing the expansion of the universe.

Beats are a different phenomenon, although related to interference. When two sound waves with very close but not identical frequencies (f1 and f2) superpose, the resulting amplitude is not constant over time: it varies periodically, sometimes reinforced, sometimes almost canceled, at a beat frequency equal to the absolute value of the difference between the two frequencies, f_beat = |f1 − f2|. Musicians exploit this phenomenon to tune two instruments by ear: as long as a slow beat can be heard, the frequencies are not yet perfectly equal; the beat disappears when f1 = f2.

Do not confuse the two phenomena: the Doppler effect really changes the perceived frequency because of relative motion, whereas beats are a variation in amplitude over time, perceived even if the source and the observer remain perfectly still.

stationary source:       . . . . . . . .   (equally spaced fronts)

source moving -->  toward the observer (on the right)

   .     .    .   .    .  . . .  . .  . .
  (fronts stretched,      (fronts compressed,
   larger lambda,          smaller lambda,
   lower frequency)        higher frequency)
                      S -->