Question: Figure 17-28 shows a moving sound source S that emits at a certain

frequency, and four stationary sound detectors. Rank the detectors

according to the frequency of the sound they detect from the

source, greatest first.

1. S is the moving source of sound.
2. 1, 2, 3 and 4 are stationary detectors.

In the given situation, the sound of the source is moving while the four detectors are stationary. Hence, the Doppler Effect is observed here. The frequency of the source changes apparently for each detector, depending on its position relative to the moving source.

The formula is as follows:

$f\text{'}=f\frac{v\pm v_D}{v\pm v_s}$

where f is the frequency and vis the velocity.

The general equation ofthedoppler effect is

$f\text{'}=f\frac{v\pm v_D}{v\pm v_s}$

The signs are chosen such that f increases when the motion is towards, and decreases when the motion is away from, the source.

In the given diagram, source S is moving towards detector 1. Hence, the observed frequency by detector 1 will be greater than f. In fact, it will be greatest among the frequencies detected bytheother three detectors.

For detector 4, the source is moving towards it, though along a different line. Hence, it will also observe the frequency f’ greater than f. But as detector 4 is not along the line, the increase will be less than that for detector 1.

For detector 3, the instantaneous position of the source S is at the same point, though along a different line. Hence, for detector 3, the observed frequency is the same as the actual frequency .

For detector 2, the source S is moving away from it. Hence, the observed frequency f will be lesser than frequency . Thus, the ranking of the detectors will be detector 1, detector 4, detector 3, and detector 2.

Therefore, the Doppler Effect is observed when there is relative motion between the source of the sound and the detector. As the source moves towards the detector, the observed frequency increases. If the source moves away from the detector, the observed frequency decreases compared to the actual frequency. This observation can be used to determine the ranking of the detectors.