Question

The pressure variation that corresponds to pain threshold (i.e., the ear can tolerate in loud sound) is about $30pa$. Velocity of the sound in water is $2103m/s$. The intensity of sound wave produced in water corresponding to loud sound is

• A. ${10}^{-12}W/m^2$
• B. $0.3\times {10}^{-3}W/m^2$
• C. $1W/m^2$
• D. ${10}^{3}W/m^2$

Answer 1

The correct option is B $0.3\times {10}^{-3}W/m^2$

Given, threshold pressure, $P_0=30Pa$

Velocity of sound in water,

$v=\sqrt{2}\times {10}^{3}m/s$

And we know, density of water,

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

So, intensity of sound wave,

$I=\frac{P_0^2}{2\rho v}$

$I=\frac{30\times 30}{2\times {10}^3\times \sqrt{2}\times {10}^3}$

$I=0.3\times {10}^{-3}W/m^2$

Final answer : (b)