question_answer

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 n. The value of n is close to:                                 [JEE Main Held on 12-4-2019 Morning] (Speed of sound in water \[=1500\text{ }m{{s}^{1}}\])

A) 499 Hz                        

B) 502 Hz

C) 507 Hz                        

D) 504 Hz

Correct Answer: B

Solution :

\[{{f}_{0}}=500Hz\]frequency recieved by A\[\Rightarrow \left( \frac{1500-5}{1500-7.5} \right){{f}_{0}}={{f}_{1}}\]and frequency recieved By B again \[\xleftarrow[{}]{{}}1500\] \[\begin{align}   & (B) \\  & 7.5m/s\xrightarrow[{}]{{}} \\ \end{align}\]                \[\begin{align}   & (A)\And \Rightarrow  \\  & \xrightarrow[{}]{{}}5m/\sec  \\ \end{align}\] \[{{f}_{2}}=\left( \frac{1500+7.5}{1500+5} \right)\times \left( \frac{1500-5}{1500-7.5} \right){{f}_{0}}=502Hz.\]