Question

Boy $A$ sings with a frequency $n$ and $B$ sings with a frequency $1/8\text{th}$ of $A$. If the intensity of sound is same and the displacement amplitude of the sound wave produced by $A$ is $a$, then the displacement amplitude of the sound wave produced by $B$ will be

• A. $2a$
• B. $4a$
• C. $6a$
• D. $8a$

Answer 1

The correct option is D $8a$

Intensity of sound,
$I=2{\pi }^2{f}^2{A}^2\rho v$, where
$f\to$ frequency of sound
$A\to$ displacement amplitude of sound
$\rho \to$ density of medium
$v\to$ speed of sound
For the same medium,
$I\propto f^2{A}^2$
So,
$\frac{I_A}{I_B}=\frac{f_A^2{A}_A^2}{f_B^2{A}_B^2}$
As, intensity is same,
$f_A^2{A}_A^2=f_B^2{A}_B^2$
$\Rightarrow n^2{a}^2=(n/8{)}^2{A}_B^2$
$\Rightarrow A_B=8a$