Question

Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after $2s$. 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, $B=2\times 10^{9}N/m^2,d=10^{3}kg/m^3$
$\therefore v=\sqrt{\frac{2\times 10^9}{10^3}}=1.414\times 10^3$
$=1414m/s$
When sound travels back to the observer, it covers twice the distance.
So, time of echo. $t=\frac{2d}{v}$
$\therefore d=\frac{tv}{2}=\frac{1414\times 2}{2}=1414m$