Q25 of 31 Page 388

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.

Given,


Operating frequency of the SONAR system, f = 40 kHz = 40 × 103 Hz


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 in this case) is moving towards it. Hence, the apparent frequency (f') received and reflected by the submarine is given by


f’ = [(v+ve)/v]f


⇒ f’ = [(1450 m s-1 + 100 m s-1)/(1450 m s-1)]×(40×103 Hz)


⇒ f’ = 42758.6 Hz


⇒ f’ = 42.759 kHz


The frequency (f’’) received by the enemy submarine is given by


f’’ = [v/(v-ve)]f’


⇒ f’’ = [(1450 m/s)/(1450 m/s – 100 m/s)]×(42758.6 Hz)


⇒ f’’ = 45925.9 Hz


⇒ f’’ = 45.93 kHz


NOTE: The Doppler effect is the phenomenon due to which there is a change in frequency or wavelength of a wave received by an observer who is moving relative to the wave source.


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