Question

The intensity of sound from a point source is 1.0 × 10⁻⁸ W m⁻² at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?

Answer 1

Given:
The intensity I₁ is 1.0 × 10⁻⁸ Wm⁻²,
when the distance of the point source $r_1$ is 5 m.
Let I₂ be the intensity of the point source at a distance ^_{$r_2$} = 25 m.
As we know,
$$\begin{gathered} I\propto \left(\frac{1}{r^2}\right). \\ \mathrm{So}, \\ \frac{I_1}{I_2}=\frac{{r_2}^2}{{r_1}^1} \\ \Rightarrow I_2=\frac{I_1{r_1}^2}{{r_2}^2} \end{gathered}$$
On substituting the respective values, we get:

$$\begin{gathered} \mathit{}{I}_2=\frac{1.0\times {10}^{-8}\times 25}{625} \\ =4.0\times {10}^{-10}\mathrm{W}/{\mathrm{m}}^2 \end{gathered}$$