When a source of sound is moving toward a stationary detection the frequency of sound perceived by the detector is not the same as the emitted by the source. In order to see this quantitatively, consider the time T elapsed between the emissions of a successive pair of spherical wave fronts (see figure 1). A Source moving with speed v s emits the first wave front. At this point, the first wave front has already traveled a distance vT, where v = 340 m/s is the speed of sound. Therefore, the wavelength detected along the direction of motion is given by the difference λ’ = vT – v s T. Using the fact that λ’f’ = λϕ = v and T = 1/f, we find that the shifted frequency f’ perceived by the detector is f’ = fv/(v – v s ).

Fig. (1)

The previous equation does not describe situations where v s v. When the source travels faster than the speed of sound, a shock wave is produced by the spherical wave fronts. Figure 2 shows the spherical wave fronts produced by such a source at equally spaced positions over an arbitrary time t. During this time, the source travels a distance v s t, and the first wave front travels a distance vt. However, in this case, the source emits each new wave after traveling beyond the front of the previously emitted wave. The wave fronts bunch along the surface of a cone called the match cone. The resulting rise and fall in air pressure as the surface of the cone passes through a point in space produces a shock wave.

Fig. (2)

(i) A roller skater carrying a portable stereo skates at constant speed an observer at rest. Which of the following accurately represents how the frequency perceived by the observer changes with time?