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 `360kmh^(-1)`. What is the frequency of sound reflected by the submarine ? Take the speed of sound in water to be `1450ms^(-1)`

Explanation

`v = 360 xx ( 5)/( 18) = 100ms^(-1)` `v =1450 ms^(-1)` `f = 40.0 kHz`
Apparent frequency `f' = f ((v+v_(s))/(v-v_(s)))`
`(v-v_(s))` is related velocity of sound w.r.t. the source
`( v + vs )` is relative velocity of sound w.r.t. the observer.
i.e. `f' = 40 xx 10^(3) xx((1450 + 100)/(1450-100))`
i.e. `f' = ( 40 xx 10^(3) xx 1550)/( 1350) Hz = 45.92 xx 10^(3) Hz`
`f' = 45.92 kHz`
i.e. `f' = 45.9 kHz`