A submarine $(A)$ travelling at $18\, km/hr$ is being chased along the line of its velocity by another submarine $(B)$ travelling at $27\, km/hr$. $B$ sends a sonar signal of $500\, Hz$ to detect $A$ and receives a reflected sound of frequency $v$. The value of $v$ is close to ... $Hz$ (Speed of sound in water $= 1500\, ms^{-1}$)
JEE MAIN 2019, Medium
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$v =$ speed of sound in water $=1500 m / s$
frequency received by $A = f$
$=\left[\frac{ V - V _{ A }}{ V - V _{ B }}\right] f _{0}=\left[\frac{1500-5}{1500-7.5}\right] f _{0}$
frequency received by $B = f ^{\prime \prime}=$
$\left[\frac{ V + V _{ B }}{ V + V _{ A }}\right] f ^{\prime}=\left[\frac{1500+7.5}{1500+5}\right]\left[ \frac{1500-5}{1500-7.5}\right] f$
$f ^{\prime \prime}=\left(\frac{1500+7.5}{1500-7.5}\right)\left(\frac{1500-5}{1500+5}\right)(500)$
$=502\; Hz$
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