# A submarine (A) travelling at $18km/hr$ is being chased along the line of its velocity by another submarine (B) travelling at $27km/hr.$ B sends a sonar signal of $500Hz$ to detect A and receives a reflected sound of frequency $v$. The value of $v$ is close to : (Speed of sound in water $=1500ms^{-1}$)  Option 1) $504Hz$ Option 2) $499Hz$ Option 3) $502Hz$ Option 4) $507Hz$

frequency of sound when source is moving towards the observer and observer is moving away from source -

$\nu {}'= \nu _{0}.\frac{C-V_{0}}{C-V_{s}}$

- wherein

$C=$ Speed of sound

$V_{0}=$ Speed of observer

$V_{s}=$ speed of source

$\nu _{0 }=$ Original frequency

$\nu {}'=$ apparent frequency

We have given that

$V_{B}=\frac{5}{18}\times 27$                                                                  $V_{A}=\frac{5}{18}\times 18=5m/s$

Frequency received by A, $f_A=f_{0}\left ( \frac{1500-5}{1500-7.5} \right )$

Frequency of the reflected sound is heard or received by $B=f_A\left ( \frac{1500+7.5}{1500+5} \right )$

$=f_{0}\left ( \frac{1500-5}{1500-7.5} \right )\left ( \frac{1500+7.5}{1500+5} \right )$

$=500\times \frac{1495}{1492.5}\times \frac{1507.5}{1505}$

$=502Hz$

Option 1)

$504Hz$

Option 2)

$499Hz$

Option 3)

$502Hz$

Option 4)

$507Hz$

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