Question

A point source emits a sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9$meter and $25$ meter, respectively from the source. The ratio of amplitudes of the wave at $P$ and $Q$ is:

• A. $25:8$
• B. $25:9$
• C. $25:16$
• D. $5:9$

Answer 1

Answer: (B)

$25:9$

The intensity $I$ of a sound wave at a distance $r$ from a point wave source is given by ,

$I\propto 1/r^2$ ,

and intensity of a wave is related with amplitude by,

$I\propto A^2$ ,

if we combine these two relations , we get ,

$A\propto 1/r$

let $A_P$ and $A_Q$ are the amplitudes of waves at point P and Q ,

therefore , $A_P/A_Q=r_Q/r_P$ ,

given $r_P=9m,r_Q=25m$ ,

therefore $A_P/A_Q=25/9$ ,

or $A_P:A_Q=25:9$