# Q.15.25 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 $1450 \: m\: s^{-1}$.

Frequency of SONAR$(\nu )$ =40 kHz

Speed of enemy submarine vo=360 km h-1 = 100 m s-1

$\\\nu _{o}=(\frac{v+v_{o}}{v})\nu \\ =\frac{1450+100}{1450}\times 40\times 10^{3}\\ =42.76\ kHz$

This is the frequency which would be observed and reflected by the enemy submarine but won't appear the same to the SONAR(source) as again there is relative motion between the source(enemy submarine) and the observer(SONAR)

The frequency which would be received by the SONAR is

$\\\nu'_{o} =\left ( \frac{v}{v-v_{s}} \right )\nu _{o}\\ =\frac{1450}{1450-100}\times 42.76\times 10^{3}\\ =45.92\ kHz$

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