Calculating Doppler Shift with Ship Sonar and Moving Targets

[jackleyt]

Homework Statement

The sound source of a ship's sonar system operates at a frequency of 23.0 kHz. The speed of sound in water 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 5.00 m/s? The ship is at rest in the water.

Homework Equations

fL= fS(v+vL)/(v+vS)

The Attempt at a Solution

I got the first part of the question, which was to find the wavelength. The wavelength is 6.44*10^(-2) m. For the second part, I calculated the frequency of the directly radiated waves and got 23,012.4 Hz. Then, I used the Doppler effect equation and got the frequency that the whale heard, which was 23077 Hz. I used that frequency to determine the reflection, and I got 23,000 Hz. The difference was 12 Hz, which was wrong. Can someone help me with what I'm doing wrong? Thanks!

 

[AtticusFinch]

A couple of things could have gone wrong here, but from what I see they aren't math related. Either:

1) The frequency of the waves reflected from the whale (the waves that the whale is producing) is 23077 Hz. 23 kHz is the frequency of the waves reflected from the whale and heard by the submarine. Small difference but a difference nonetheless.

2) The wavelength you calculated in a) was in a different medium than water.

 

[jackleyt]

Thanks! It was the latter of the two.