Question

A whale uses the equivalent of sonar to locate objects underwater. The whale is swimming away from a stationary shipwreck at the bottom of the ocean at a speed of 6 m/s while emitting a call at 50 Hz. The speed of sound in sea water is 1500 m/s. What frequency does the whale heat reflected from the object underwater?

Answer 1

Let vs be the velocity of the sound source, be the actual frequency of sound source, vl be the velocity of the listener, be the frequency of the listener and v be the velocity sound in the medium, then by equation of Doppler effect, the apparent frequency () heard by the listener is given by

When the source and listener id receding, vs is negative and vl is positive. Here source is the whale and listener is the shipwrek.

Given,

Velocity of whale is 6 m/s. So vs = -6m/s

Frequency emitted by whale is 50 Hz. So = 50 Hz

Speed of sounf in sea water is 1500 m/s. So v = 1500 m/s

Shipwrek is stationary. So vl = 0

Substituting the values in the above equation,

The shipwrek recieves a frequency of 49.80 Hz.

Now this frequency of 49.80Hz is reflected back to the whale. In this situation whale is the reciever and shipwrek is the source.

Here also shipwrek is stationary. So vs = 0

Velocity of whale is 6 m/s. So vl = 6m/s

Frequency emitted from shipwrek is 49.80 Hz. So = 49.80 Hz

Substituting the values in the above equation,

So the whale gets reflected back a frequency of 49.60 Hz