Question

A submarine $A$ travelling at $18kmh{r}^{-1}$ is being chased along the line of its velocity by another submarine $B$ travelling at $27kmh{r}^{-1}$ . $B$ sends a sonar signal of $500Hz$ to detect $A$ and receives a reflected sound of frequency $v$ . The value of $v$ is closed to (Speed of sound in water $1500m{s}^{-1}$ )

• A. $504Hz$
• B. $499Hz$
• C. $502Hz$
• D. $507Hz$

Answer 1

Answer: (C)

$V_A=18km{h}^{-1}=5m{s}^{-1}$ ; $V_B=27km{h}^{-1}=7.5m{s}^{-1}$
Frequency received by $A$ , $f_A=f_0\left(\frac{1500-5}{1500-7.5}\right)$
Frequency of reflected wave as heard by $B$ .
${\mathrm{f}}_{\mathrm{B}}^{\prime }={\mathrm{f}}_{\mathrm{A}}\left(\frac{1500+7.5}{1500+5}\right)$
$=f_0\left(\frac{1500-5}{1500-7.5}\right)\left(\frac{1500+7.5}{1500+5}\right)$
$=500\left(\frac{1495}{1492.5}\right)\left(\frac{1507.5}{1505}\right)$
$=501.67Hz\approx 502Hz$