Question

A pressure of 100 kPa causes a decrease in volume of water by $5\times {10}^{-3}$ %. The speed of sound in water is :

• A. $1414m{s}^{-1}$
• B. $1000m{s}^{-1}$
• C. $2000m{s}^{-1}$
• D. $3000m{s}^{-1}$

Answer 1

The correct option is A $1414m{s}^{-1}$

$V=\sqrt{\frac{K}{\rho }}$

$K=\frac{\delta P}{\delta V/V}$

$K=\frac{100\times {10}^3}{5\times {10}^{-3}\times {10}^{-2}}$

$=\sqrt{\frac{100\times {10}^3}{5\times {10}^{-5}}}$

$=\sqrt{20\times {10}^8}$

$\rho ={10}^{3}kg/m^3$

Putting these values

$V=\sqrt{\frac{20\times {10}^8}{{10}^3}}$ = 1414m/s