Question

The sound source of a ship’s sonar system operates at a frequency of 22.0 kHz . The speed of sound in water (assumed to be at a uniform 20∘C) is 1482 m/s . What is the difference in frequency between the directly radiated waves and the waves reflected from a whale traveling straight toward the ship at 4.95 m/s ? Assume that the ship is at rest in the water.

Answer 1

147.456077993 Hz

Step-by-step explanation:

`f_0` = Frequency of the sonar = 22 kHz

`v_w` = Velocity of the whale = 4.95 m/s

v = Speed of sound in water = 1482 m/s

The difference in frequency is given by

`\Delta f=f_0*(2v_(w))/(v-v_w)\\\Rightarrow \Delta f=22000*(2* 4.95)/(1482-4.95)\\\Rightarrow \Delta f=147.456077993\ Hz`

The difference in frequency is 147.456077993 Hz