Question

If the frequency of sound produced by a siren increases from $400\text{Hz}$ to $1200\text{Hz}$ keeping the amplitude constant. The ratio of the intensity of sound produced at frequency $1200\text{Hz}$ and $400\text{Hz}$ will be

• A. $1:1$
• B. $1:3$
• C. $3:1$
• D. $9:1$

Answer 1

The correct option is D $9:1$

We know that the intensity of sound is given by,
$I=\frac{1}{2}\rho {\omega }^2{A}_o^{2}v$,
where, $\rho$ is the density of medium, $\omega$ is the angular frequency of sound, $A_o$ is the displacement amplitude of particles of medium and $v$ is the speed of sound.
$\Rightarrow I=2{\pi }^2{f}^2\rho A_o^{2}v$
$[\omega =2\pi f]$
As medium is same and amplitude remain constant.
$\Rightarrow I\propto f^2$
So,
$\frac{I_1}{I_2}=\frac{f_1^2}{f_2^2}$
$\Rightarrow \frac{I_1}{I_2}=\frac{{1200}^2}{{400}^2}=\frac{9}{1}=9:1$
$\Rightarrow I_1:I_2=9:1$