The Doppler effect is likely a phenomenon you have encountered before. When an ambulance, police car, or racecar travels past you, the sound you hear changes pitch. This happens because the motion of the vehicle compresses or extends the
Fig. 1 Left: An ambulance at rest emitting a sound wave from its siren. The wavelength λ0 and frequency f0 of the sound wave is the same in all directions. Right: Now the ambulance is moving to the right. The sound wave in front of the ambulance is compressed, which means the perceived wavelength is smaller and the perceived frequency is larger (higher pitch). The sound wave behind the ambulance is expanded, which means the perceived wavelength is larger and the perceived frequency is smaller (lower pitch) .
sound waves. Figure 1 shows the sound waves emitted by a stationary ambulance (left) and a moving ambulance (right). Let’s focus on the stationary ambulance.
Imagine that you are standing in front of or behind the ambulance. The wavelength of the sound wave that hits your ear is the same for both scenarios, so you would hear the same pitch independent of where you are standing. Now, imagine the ambulance is moving. If you were standing in front of the ambulance (OK, maybe a bit to the side . . . we don’t want you to get hit, even in a thought experiment(,
the wavelength of the sound wave that reaches your ear is shorter compared to the stationary ambulance. If you were standing behind the moving ambulance, the wavelength is longer compared to the stationary ambulance. The formula that relates the frequency (pitch) that you hear to the wavelength should look really familiar.
It is 
, where 
is the speed of sound in air (replace with
