Question

gg The sound source of a ship’s sonar system operates at a frequency of 22.0 kHzkHz . The speed of sound in water (assumed to be at a uniform 20∘C∘C) is 1482 m/sm/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/sm/s ? Assume that the ship is at rest in the water.

Answer 1

Δf = 73.72Hz

Step-by-step explanation:

In order to calculate the difference in frequency between the direct waves and the reflected waves, you first take into account the Doppler's effect for an observer getting closer to the source:

`f'=f((v+v_o)/(v-v_s))` (1)

You can assume that the reflected waves come from a source "the whale". Then you have:

f': frequency of the reflected waves = ?

f: frequency of the source = 22.0*kHz = 22.0*10^3 Hz

v: speed of the sound in water = 1482m/s

vs: speed of the source = 4.95m/s

vo: speed of the observer = 0m/s

You replace the values of the parameters in the equation (1):

`f'=(22.0*10^3Hz)((1482m/s)/(1482m/s-4.95m/s))=22073.72Hz`

Then, the difference in frequency is:

`\Delta f = f'-f=22000Hz-22073.72Hz=73.72Hz`