Question

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/hr. What is the frequency of sound reflected by the submarine? Take the speed of sound in water to be 1450 m/s.

Answer 1

Operating frequency of the SONAR system, ν = 40 kHz
Speed of the enemy submarine, $v_e=360$ 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:
$v^{\prime }=\left(\frac{v+v_e}{v}\right)v=\left(\frac{1450+100}{1450}\right)\times 40=42.76kHz$
The frequency (v') received by the enemy submarine is given by the relation:
$v^{\prime \prime }=\left(\frac{v}{v+v_s}\right)v^{\prime }$
where, $v_s=100m/s$
$\therefore v^{\prime \prime }=\left(\frac{1450}{1450-100}\right)\times 42.76=45.93kHz$