d
Operating frequency of the \(SONAR\) system, \(v=40 \,kHz\)

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 apparen frequency ( \(v^{\prime}\) ) received and reflected by the submarine is given by the relation:

\(v^{\prime}=\left(\frac{v+v_{e}}{v}\right) \,v\)

\(=\left(\frac{1450+100}{1450}\right) \times 40=42.76\, kHz\)

The frequency \(\left(v^{\prime \prime}\right)\) received by the enemy submarine is given by the relation:

\(v^{\prime \prime}=\left(\frac{v}{v+v_{s}}\right) v^{\prime}\)

Where, \(v_{ s }=100 \,m / s\)

\(\therefore v^{\prime \prime}=\left(\frac{1450}{1450-100}\right) \times 42.76=45.93 \,kHz\)