Question

Volumetric strain of water is 5 x 10^-5 at 10 N m^-2 pressure. If density of water is 1 x 10³ kg m^-3, then determine the speed of sound in water.

Answer 1

Volumetric strain = 5 x 10⁵; ρ = 1 x 10³ kg m^-3; v = ?
Bulk modulus of the water

\(\beta = \frac{Volume\ stress}{Volumetric\ strain} = \frac{10^5}{5\times10^{-5}} = 0.2\times1010\) 

= 2 x 10⁹ N m^-2

^{\(\therefore \ v =\sqrt{\frac{\beta}{\rho}} = \sqrt{\frac{2\times10^9}{10^3}} = \sqrt{2\times10^6}\)}

= 1.4142 x 10³

= 1414.2 ms^-1

Based on Speed of Sound in Gases