Q. 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
Explanation
(c) $I = 2\pi^{2}a^{2}n^{2}v\rho \Rightarrow I \propto a^{2}n^{2}$
$\Rightarrow \frac{I_{1}}{I_{2}} = \left( \frac{a_{1}}{a_{2}} \right)^{2} \times \left( \frac{n_{1}}{n_{2}} \right)^{2} = \left( \frac{1}{2} \right)^{2} \times \left( \frac{1}{1/4} \right)^{2}$
$\Rightarrow I_{2} = \frac{I_{1}}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.