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

Here true frequency of SONAR system `v=40.0Hz`, speed of sound in water `v=1450ms^(-1)`, speed of enemy submarine towards the SONAR `v_(0)=360kmh^(-1)=360=(5)/(18)ms^(-1)=100ms^(-1)`.
As the source is at rest and observer is in motion towards the source, apparent frequency received by observer (enemy submarine) will be
`v'=(v+v_(0))/(v),v=(1450+100)/(1450)xx40.0kHz=42.76kHz`
Then the frequency is reflected by enemy submarine (which now behaves as source, moving with a velocity
`vs=-100ms^(-1)`) and is observed by SONAR. hence SONAR. hence, frequency as felt by SONAR system.
`v''=(v)/(v-v_(S)),v'=(1450)/(1450-100)xx42.76kHz=45.9kHz`