Physics - Wave on String Question with Solution | TestHub

For a point source, the intensity $I$ of a sound wave at a distance $r$ is inversely proportional to the square of the distance.

$I\propto \frac{1}{r^2}$

The intensity is also directly proportional to the square of the amplitude $A$.

$I\propto A^2$

From the above two relations, we get:

$A^2\propto \frac{1}{r^2}\Rightarrow A\propto \frac{1}{r}$

Let the amplitude at distance $r$ be $A_1=A$ and at distance $2r$ be $A_2$.

$\frac{A_2}{A_1}=\frac{r}{2r}=\frac{1}{2}$

$A_2=\frac{A}{2}$

Answer: $\frac{A}{2}$