Question

an increase in pressure of hundred kilo Pascal causes a certain volume of water to decrease by 5 into 10 raise to minus 3% of its original volume .the speed of sound in water is close to​

Answer 1

you mean, pressure increases , ∆P = 100kPa = 10^5 Pa .......(1)

volume change ( decreases) = -5 × 10^-3 % [ here negative sign shows that volume is decreased ]

or, change in volume/original volume × 100 = -5 × 10^-3 %

or, ∆V/V = -5 × 10^-5 ........(2)

now, bulk modulus , $\beta=-\frac{\Delta P}{\frac{\Delta V}{V}}$

= -(10^5)/(-5 × 10^-5)

= 0.2 × 10^10

= 2 × 10^9 N/m²

now, speed of sound in water , $v=\sqrt{\frac{\beta}{\rho}}$

where, $\rho$ is density of water.

e.g., $\rho=1000Kg/m^3$

so, v = √{2 × 10^9/1000} = √{2 × 10^6}

= √2 × 10³ = 1.414 × 1000 = 1414 m/s

hence, speed of sound in water is 1414 m/s