Question

A SONAR system fixed in a submarine operates at a frequency 40.0 kHz. An enemy submarine moves towards the SONAR with a speed of 360 km h¯¹. What is the frequency of sound reflected by the submarine ? Take the speed of sound in water to be 1450 m s¯¹.

Answer 1

Given, the frequency of SONAR is 40.0 kHz, the speed of the enemy’s submarine is 360  km/h and the speed of sound in water is 1450 m/s .

The apparent frequency received by enemy’s submarine is given by the equation,

ν ′ =( v+ v 0 v )ν

Substituting the values in the above equation, we get:

ν ′ =( 1450 m/s +360  km/h × 5 18 1450 m/s )40.0 kHz =42.76 kHz

The frequency of the SONAR received by the enemy is given by the equation,

ν ″ =( v v− v 0 ) ν ′

Substituting the values in the above equation, we get:

ν ″ =( 1450 m/s 1450 m/s −360  km/h × 5 18 )42.76 kHz =45.9 kHz

Thus, the frequency of SONAR received by the enemy’s submarine is 45.9 kHz.