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 \(= 1500\, ms^{-1}\))

Pick an option to check your answer.

Verified Solution

Answer & Solution

Correct Answer

(B) \(502\)

Detailed explanation

\(v =\) 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 \(B = f ^{\prime \prime}=\)

\(\left[\frac{ V + V _{ B }}{ V + V _{ A }}\right] f ^{\prime}=\left[\frac{1500+7.5}{1500+5}\right]\left[ \frac{1500-5}{1500-7.5}\right] f\)

\(f ^{\prime \prime}=\left(\frac{1500+7.5}{1500-7.5}\right)\left(\frac{1500-5}{1500+5}\right)(500)\)

\(=502\; Hz\)

Same subject

From JEE Mains