Figure: Stationary and moving Wave Sources

Stationary Sound Source

The first movie 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 second movie 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 v_s = 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 (v_s = v, or Mach 1). The speed of sound in air at sea level is about 340 m/s or about 1200 km/h. 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. Jet pilots flying at Mach 1 report that there is a noticeable "wall" or "barrier" which must be penetrated before achieving supersonic speeds. This "wall" is due to the intense pressure front, and flying within this pressure front produces a very turbulent and bouncy ride.

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. As you watch the animation, notice the clear formation of the Mach cone, the angle of which depends on the ratio of source speed to sound speed. It is this intense pressure front on the Mach cone that causes the shock wave known as a sonic boom as a supersonic aircraft passes overhead. The shock wave advances at the speed of sound v, and since it is built up from all of the combined wave fronts, the sound heard by an observer will be quite intense. A supersonic aircraft usually produces two sonic booms, one from the aircraft's nose and the other from its tail, resulting in a double thump.

Credit: Daniel A. Russell, Kettering University

http://www.kettering.edu/~drussell/Demos/doppler/doppler.html