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A sonar system fixed in a submariene ope...

A sonar system fixed in a submariene operatres at a frequency 40KHz. An enemey submarine moves towards the sonar with a speed of `360kmh^(-1)`. What is the frequency of sound reflected by the submarine? Speed of sound in water `1450ms^(-1)?`

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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`
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