The volumetric strain of water at a pressure of $10^5\ \mathrm{Nm}^{-2}$ is $5\times10^{-5}$. Determine the…
The volumetric strain of water at a pressure of $10^5\ \mathrm{Nm}^{-2}$ is $5\times10^{-5}$. Determine the speed of sound in water. Density of water is $10^3\ \mathrm{kg\ m}^{-3}$.
Solution
Sol. Bulk modulus of water, $B=\dfrac{\text{Normal stress}}{\text{Volumetric strain}}=\dfrac{10^5}{5\times10^{-5}}=2\times10^9\ \mathrm{Nm}^{-2}$
$\therefore$ Density of water, $\rho=10^3\ \mathrm{kg\ m}^{-3}$ (Given)
$\therefore$ Speed of sound in water, $v=\sqrt{\dfrac{B}{\rho}}$
$\Rightarrow\quad v=\sqrt{\dfrac{2\times10^9}{10^3}}=1.41\times10^3\ \mathrm{ms}^{-1}$
Answer: $1.41\times10^3$ ms$^{-1}$