Question

In a sound wave, to increase the intensity by a factor of $10$, pressure amplitude must be changed by a factor of:

• A. $\sqrt{20}$
• B. $\sqrt{10}$
• C. $10$
• D. $10\sqrt{2}$

Answer 1

The correct option is B $\sqrt{10}$

As we know, intensity of sound source is related to pressure amplitude given by,

$I=\frac{1}{2}\frac{P_0^2}{\rho v}$

$I\propto P_0^2$

$\frac{I^{\prime }}{I}=\frac{P_0^{\prime }2}{P_0^2}$

$P_0^{\prime }=P_0\sqrt{\frac{I^{\prime }}{I}}$

When intensity is increased by factor of $10$,

$P_0^{\prime }=P_0\sqrt{10}$

So, pressure amplitude changed by factor of $\sqrt{10}$

Final answer: (a)