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A SONAR system fixed in a submarine oper...

A SONAR system fixed in a submarine operates at a frequency 40.0kHz. 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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(i) When source of ultrasonic (SONAR system) is at rest and detector (enemy submarine) moves towards stationary source.

We have `(f _(L))/( v + v _(L)) = (f _(S))/(v + v _(S))`
`therefore (f _(L))/( 14 50 + 100) = (40)/(1450 + 0)`
`therefore f _(L) = (1550 )/(1450) xx 40 = 42.7886kHz`
(ii) When ultrasonic waves are reflected by enemy submarine, it becomes imaginary source of reflected waves of frequency `f _(L) = 42.7586kHz,` moving towards stationary detector (SONAR system).

We have, `(f._(L))/(v + v _(L)) = (f ._(S))/( v + v ._(S))`
`therefore (f ._(L))/(v + v _(L)) = (f ._(L))/( v + v._(S)) (because f ._(S) = f _(L))`
`therefore (f ._(L))/( 1450 +0) = (42.7586)/(1450 -100)`
`implies f._(L) = (1450)/(1350) xx 42 .7586 =45.93` kHz
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