Question

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

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

Answer 1

Answer: (C)

$V_{A}=18kmh^{- 1}=5 \, ms^{- 1}$ ; $V_{B}=27kmh^{- 1}=7.5ms^{- 1}$
Frequency received by $A$ , $f_{A}=f_{0}\left(\frac{1500 - 5}{1500 - 7 .5}\right)$
Frequency of reflected wave as heard by $B$ .
$\mathrm{f}_{\mathrm{B}}^{\prime}=\mathrm{f}_{\mathrm{A}}\left(\frac{1500+7.5}{1500+5}\right)$
$=f_{0}\left(\frac{1500 - 5}{1500 - 7.5}\right)\left(\frac{1500 + 7.5}{1500 + 5}\right)$
$=500\left(\frac{1495}{1492.5}\right)\left(\frac{1507.5}{1505}\right)$
$=501.67Hz\approx 502Hz$