Answer:
a) The frequency detected by the submarine B, f' = 1595 Hz
b) The frequency of the reflected wave detected by the A is, f'' = 6021 Hz
Explanation:
Given data,
The speed of submarine A, v = 15.8 m/s
The speed of submarine B, v' = 8.63 m/s
The SONAR wave travels at a speed of V = 1522 m/s
The formula for Doppler effect is,
![f' = \frac{V+v'}{V-v} f](https://tex.z-dn.net/?f=f%27%20%3D%20%5Cfrac%7BV%2Bv%27%7D%7BV-v%7D%20f)
Substituting the given values above,
![f' = \frac{1522+8.63}{1522-15.8} 1570](https://tex.z-dn.net/?f=f%27%20%3D%20%5Cfrac%7B1522%2B8.63%7D%7B1522-15.8%7D%201570)
f' = 1595 Hz
The reflected SONAR has the frequency of, f' = 1595 Hz
Therefore, the frequency of the reflected wave at A is given by the formula,
![f'' = \frac{V+v}{V-v'} f'](https://tex.z-dn.net/?f=f%27%27%20%3D%20%5Cfrac%7BV%2Bv%7D%7BV-v%27%7D%20f%27)
![f'' = \frac{1522+15.8}{1522-8.63} 1595](https://tex.z-dn.net/?f=f%27%27%20%3D%20%5Cfrac%7B1522%2B15.8%7D%7B1522-8.63%7D%201595)
f'' = 6021 Hz
Hence, the reflected wave has the frequency of f'' = 6021 Hz