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A SONAR system fixed in a submarine ope...

A SONAR system fixed in a submarine operates at a frequency40.0 kHz. An enemy submarine moves towards the SONAR with a speed of `360km h^(-1)`.What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be `1450ms^(-1)`

Text Solution

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Here, frequency of SONAR,
`v=40 KHz =40 xx 10^(3) Hz`
Speed of observer `//` enemy's submarine
`v_(1) = 360 km//h`
`= 360xx ( 5)/( 18) m//s = 100 m//s `
Speed of sound wave in water,`v= 1450 m//s`. As the source is at rest & observer is moving towards the source , therefore, apparent frequency receivedby enemy submarine.
`v^(1) = ((v+ v_(l))v)/(v)`
`((1450+100)40 xx10^(3)Hz)/(1450)`
`= 4.27 xx10^(4) Hz`
This frequency is reflected by enemy submarine ( source) and is observed by SONAR . Therefore in this case.
`v_(s) =360 km//s= 100 m//s , v_(l) = 0`
` :. ` Apparent frequency , `v^(11)= (vxx v)/(v-v_(s))`
`= ( 1450 xx 4.276 xx10^(4))/(1450-10)`
`= 4.59 xx 10^(4) Hz= 45.9Hz`
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