A submarine (A) travelling at $18 \mathrm{~km} / \mathrm{hr}$ is being chased along the line of its

Question

A submarine (A) travelling at $18 \mathrm{~km} / \mathrm{hr}$ is being chased along the line of its velocity by another submarine $(B)$ travelling at $27 \mathrm{~km} / \mathrm{hr}$. B sends a sonar signal of 500 Hz to $\operatorname{detect} A$ and receives a reflected sound of frequency $v$. The value of $v$ is close to (speed of sound in water $=1500 \mathrm{~m} \mathrm{~s}^{-1}$ )\

Professor PC Thomas Classes · Answer

(d)$5 \mathrm{~m} / \mathrm{s}$\ $18 \mathrm{~km} / \mathrm{h}=18 	imes \frac{5}{18}=5 \mathrm{~m} / \mathrm{s}$\ $27 \mathrm{~km} / \mathrm{h}=27 	imes \frac{5}{18}=7.5 \mathrm{~m} / \mathrm{s}$\ Frequency received by $A$, $$ f_{A}=\frac{(1500-5)}{(1500-7.5)} 	imes 500 $$ Frequency received by $B$,\ $f_{B}=f_{A} 	imes \frac{(1500+7.5)}{(1500+5)}$\ $\Rightarrow f_{B}=\frac{(1500-5)}{(1500-7.5)} 	imes \frac{(1500+7.5)}{(1500+5)} 	imes 500$\ $=502 \mathrm{~Hz}$\