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).

A SONAR system fixed in a submarine operates at a frequency 40.0kHz. A

1.	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).
Answer» Solution :(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