The Doppler Effect

The sudden change in pitch of a car horn as a car passes by (source motion) or in the pitch of a boom box on the sidewalk as you drive by in your car (observer motion) was first explained in 1842 by Christian Doppler. His Doppler Effect is the shift in frequency and wavelength of waves which results from a source moving with respect to the medium, a receiver moving with respect to the medium, or even a moving medium.

The perceived frequency (f ´) is related to the actual frequency (f₀) and the relative speeds of the source (v_s), observer (v_o), and the speed (v) of waves in the medium by

The animations below will illustrate this phenomena for a moving source and stationary observer.

Stationary Sound Source

The movie at left shows a stationary sound source. Sound waves are produced at a constant frequency f0, and the wavefronts propagate symmetrically away from the source at a constant speed v, which is the speed of sound in the medium. The distance between wavefronts is the wavelength. All observers will hear the same frequency, which will be equal to the actual frequency of the source.

Source moving with v_source < v_sound ( Mach 0.7 )

In the movie at left the same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed vs = 0.7 v (Mach 0.7). The wavefronts are produced with the same frequency as before. However, since the source is moving, the center of each new wavefront is now slightly displaced to the right. As a result, the wavefronts begin to bunch up on the right side (in front of) and spread further apart on the left side (behind) of the source. An observer in front of the source will hear a higher frequency f ´ > f0, and an observer behind the source will hear a lower frequency f ´ < f0.

Source moving with v_source = v_sound ( Mach 1 - breaking the sound barrier )

Now the source is moving at the speed of sound in the medium (vs = v, or Mach 1). The speed of sound in air at sea level is about 340 m/s or about 750 mph. The wavefronts in front of the source are now all bunched up at the same point. As a result, an observer in front of the source will detect nothing until the source arrives. The pressure front will be quite intense (a shock wave), due to all the wavefronts adding together, and will not be percieved as a pitch but as a "thump" of sound as the pressure wall passes by.

Source moving with v_source > v_sound (Mach 1.4 - supersonic)

The sound source has now broken through the sound speed barrier, and is traveling at 1.4 times the speed of sound (Mach 1.4). Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer actually hears the sound it creates.