Question

A point source emits sound equally in all directions in a non absorbing medium. Two points P and Q are at distances of 9m and 25m respectively from the source. The ratio of the amplitude of the waves at P and Q is?
A. $5:3$
B. $3:5$
C. $25:9$
D. $625: 81$

Answer 1

Hint: This is a non absorbing medium, so there will be no loss of energy of the wave as it propagates through the medium. Also, the sound is directed in all directions equally so we do not have to consider the direction. Here we need to find out the ratio of the amplitude and not the intensities.

Complete step by step answer:
We know for a wave propagating through a non-absorbing medium, the amplitude at any point from the source is given by the relation: \[A\alpha \dfrac{1}{x}\], where A is the amplitude and x is the distance from the source to the point where the amplitude is to be determined.
Given \[{{x}_{1}}\]= 9m and \[{{x}_{2}}\]= 25 m
Putting the values, we get,
$A\alpha \dfrac{1}{x} \\
\Rightarrow \dfrac{{{A}_{1}}}{{{A}_{2}}}=\dfrac{{{x}_{2}}}{{{x}_{1}}} \\
\therefore \dfrac{{{A}_{1}}}{{{A}_{2}}}=\dfrac{25}{9}$

So, the correct option is C.

Additional information:
The amplitude of a sound wave is the measure of the height of the wave. The amplitude of a sound wave can be defined as the loudness or the amount of maximum displacement of vibrating particles of the medium from their mean position when the sound is produced. It is the distance between crest or trough and the mean position of the wave.

Note: The amplitude of a wave is related to the amount of energy it carries. A high amplitude wave carries a large amount of energy; a low amplitude wave carries a small amount of energy. The average amount of energy passing through a unit area per unit of time in a specified direction is called the intensity of the wave. As the amplitude of the sound wave increases, the intensity of the sound increases.