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 360 km h-1. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m s-1.
Operating frequency of the SONAR system, v = 40 kHz
Speed of the enemy submarine, ve = 360 km/h = 100 m/s
Speed of sound in water, v = 1450 m/s
The source is at rest and the observer (enemy submarine) is moving toward it. Hence, the apparent frequency (v') received and reflected by the submarine is given by the relation:
v' = ( v + ve / v ) v
= ( 1450+ 100 / 1450 ) x 40 = 42.76 kHz
The frequency (v'') received by the enemy submarine is given by the relation:
v'' = ( v / v + vs) v'
where, vs = 100 m/s
∴ v'' = (1450 / 1450-100) x 42.76 = 45.93 kHz
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