Question

Compressional wave impulses are sent to the bottom of sea from a ship and the echo is heard after $4\text{s}.$ If bulk modulus of water is $2\times {10}^9{\text{Nm}}^{-2}$ and the mean temperature is $4^{\circ }\text{C}$, then depth of the sea is

• A. $2000\times {10}^3\text{m}$
• B. $2828\text{m}$
• C. $1414\text{m}$
• D. $707\text{m}$

Answer 1

Answer: (B)

$2828\text{m}$

$V_s=\sqrt{\frac{E}{\rho }}$,

$E=2\times {10}^9{\text{Nm}}^{-2}$,

$\rho =1000{\text{kgm}}^{-3}$

$V_s=\sqrt{\frac{2\times {10}^9}{1000}}=1414{\text{ms}}^{-1}$

Since it took $4\text{sec},$ to reach and reflect back for the sound wave,

sound will travel twice of the depth.

$2d=4\times 1414\text{m}$

$d=2828\text{m}$

Option 'B' is correct.