Question

Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after $2 s$. If bulk modulus of elasticity of water is $2 \times 10^{9} \,N / m ^{2}$ and mean temperature is $4^{\circ} C$, the depth of the sea will be

• A. 1014 m
• B. 1414 m
• C. 2828 m
• D. none of these

Answer 1

Answer: (B)

The speed of sound (longitudinal waves) in water is given by $v=\sqrt{\frac{B}{d}}$
where $B$ is bulk modulus of water and $d$ is density.
Given, $B=2 \times 10^{9} \,N / m ^{2}, d=10^{3} \,kg / m ^{3}$
$\therefore v=\sqrt{\frac{2 \times 10^{9}}{10^{3}}}=1.414 \times 10^{3}$
$=1414\, m / s$
When sound travels back to the observer, it covers twice the distance.
So, time of echo. $t=\frac{2 d}{v}$
$\therefore d=\frac{t v}{2}=\frac{1414 \times 2}{2}=1414\, m$