Question

The distance between a sound source and a listener is decreased to half the initial distance. What is the change in the amplitude of the sound heard?
It decreases by half the initial amplitude.
It increases by four times the initial amplitude.
It decreases to one fourth the initial amplitude.
It increases by two times the initial amplitude

Answer 1

"It increases by four times the initial amplitude" is the one among the following choices given in the question that is the change in the amplitude of the sound heard. The correct option among all the options that are given in the question is the second option. I hope that this is the answer that has come to your desired help.

Answer 2

Answer:

It increases by four times the initial amplitude.

Explanation:

The amplitude of a sounde is inversely proportional to the square of the distance between the listener and the sound source:

$A \sim \frac{1}{r^2}$

In this problem, the distance is decreased to hald the initial distance, so we can write

$r'=\frac{r}{2}$

therefore, the new amplitude will be

$A' \sim \frac{1}{r'^2}=\frac{1}{(\frac{r}{2})^2}=4 \frac{1}{r^2}=4 A$

So, the amplitude increases by a factor 4.