Question

If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be

• A. Increased by a factor of 2
• B. Decreased by a factor of 2
• C. Decreased by a factor of 4
• D. Unchanged

Answer 1

The correct option is C

Decreased by a factor of 4

$I=2{\pi }^2{a}^2{n}^{2}v\rho \Rightarrow I\propto a^2{n}^2\Rightarrow \frac{I_1}{I_2}={\left(\frac{a_1}{a_2}\right)}^2\times {\left(\frac{n_1}{n_2}\right)}^2$

= ${\left(\frac{1}{2}\right)}^2\times {\left(\frac{1}{\frac{1}{4}}\right)}^2\Rightarrow I_2=\frac{I_1}{4}$