Question

If at some point, the amplitude of a sound wave becomes double and the frequency becomes one fourth, then at that point, the intensity of sound will:

• A. Become double
• B. Become half
• C. Become one fourth
• D. Remain unchnaged

Answer 1

The correct option is C Become one fourth

$I=2{\pi }^2{f}^2{S}_0^2\rho v$
where $f=$ frequency
$S_0=$ amplitude
Hence $I\propto f^2{S}_0^2$
$I_1=k{f}_1^2(S_0{)}_1^2\to (1)$

Given, $(S_0{)}_2=2(S_0{)}_1\to \left(2\right)$
& $f_2=\frac{f_1}{4}\to \left(3\right)$

$\Rightarrow I_2=k{f}_2^2(S_0{)}_2^2\to (4)$

Taking ratio of (1) & (2),
$\frac{I_1}{I_2}={\left(\frac{f_1}{f_2}\right)}^2{\left(\frac{(S_0{)}_1}{(S_0{)}_2}\right)}^2$
$=(4{)}^2{\left(\frac{1}{2}\right)}^2=\frac{16}{4}=4$
$\therefore I_2=\frac{I_1}{4}$