A SONAR system fixed in a submarine operates at a frequency 40.0kHz. 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 `ms^(-1)`.

Explanation

Operating frequency of the SONAR system, ν = 40 kHz
Speed of the enemy submarine, v`_(e) = 360 km//h = 100 m//s`
Speed of sound in water, v = 1450 m/s
The source is at rest and the observer (enemy submarine) is moving toward it. Hence, the apparent frequency `(v'')` received and reflected by the submarine is given by the relation:
`v((v+v_(e))/(v))v`
`=((1450+100)/(1450))xx40=42.76 kHz`
The frequency (v'') received by the enemy submarine is given by the relation:
`v''=((v)/(v+v_(s)))v'`
Where,`v_(s)=100 m//s`
`:. v''=((1450)/(1450-100))xx42.76=45.93 kH.`