Question

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.

Short answer

Answer

The rank of detectors, according to the frequency of sound they detect, greatest first is detector 1, detector 4, detector 3, and detector 2.

Step-by-step solution

Step 1: Stating given data

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

Determining the concept

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.

Determining the rank of detectors according to the frequency of sound they detect, greatest first

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.