Question

An ultrasonic sonar system emits ultrasonic waves that have a frequency of 600 kHz. The waves reflect from a plane that is moving at 36.0% of the speed of sound, directly toward the sonar system. Find the frequency of the waves that are detected by the sonar system, after they reflect from the plane.

Answer 1

Solution:-

Observer is the moving plane and source is sonar system

f' = (v + v_o )f / v

where v is speed of sound, f is original frequency, f' is observed frequency, v_o is speed of observer

v_o = 36% of speed of sound = 0.36v

f' = (v + 0.36v)f / v

f' = 1.36vf / v

f' = 1.36*f

f' = 1.36*600

f' = 816Hz

This the frequency observed by moving source. Howver ,we need frequency observed by sonar. so there will be one more doppler shift.

f'' = 816( v / v - 0.36v)

f'' = 816 / 0.64

f'' = 1275 kHz