The Doppler Effect

When a sound source moves toward you, it keeps catching up a little to its own sound waves, squeezing them closer together in front — so you hear a higher pitch. When it moves away, the waves stretch out behind it, so the pitch drops. This is why a siren sounds higher as it approaches and lower as it passes and speeds away.

f_obs = f · c / (c − v_s)

  • f_obs — observed frequency (Hz): the pitch you actually hear
  • f — source frequency (Hz): the pitch the source emits when standing still
  • c — speed of sound (m/s): how fast sound waves travel through the air
  • v_s — source speed (m/s): how fast the source moves toward you

An ambulance siren emits a steady 320 hertz tone while driving toward you at 20 meters per second. Sound travels at 340 meters per second. What frequency do you hear?

  • f = 320 Hz
  • c = 340 m/s
  • v_s = 20 m/s
  1. f_obs = f · c / (c − v_s)
  2. f_obs = 320 Hz · 340 / (340 − 20) = 320 Hz · 340 / 320

f_obs = 340 Hz

A quieter siren emits 160 hertz while approaching you at the same 20 meters per second, with sound still traveling at 340 meters per second. What frequency do you hear?

  • 170 Hz
  • 150 Hz
  • 180 Hz

If that same ambulance instead drove away from you at 20 meters per second, would the pitch you hear be higher, lower, or the same as the siren's true 320 hertz?

  • Higher than 320 Hz
  • Lower than 320 Hz
  • The same, 320 Hz