Question

When excess pressure of $2\times {10}^{5}Pa$ is applied on water, the fractional change in its volume is approximately ${10}^{-n}$. Take speed of sound in water as $1400m/s$ and density of water as $1000kg/m^3$, then $n$ is

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is D 4

$v=\sqrt{\frac{\beta }{\rho }}\Rightarrow v^2\rho =\beta$ (where $\beta$ is bulk modulus of that medium)
$\beta =\frac{V\Delta P}{\Delta V}\Rightarrow \frac{\Delta V}{V}=\frac{\Delta P}{\beta }=\frac{\Delta P}{v^2\rho }$

$\frac{\Delta V}{V}=\frac{2\times {10}^5}{(1400{)}^2\times {10}^3}=\frac{50}{49}{.10}^{-4}\approx {10}^{-4}$

$⟹n=4$