Question

The intensity of sound from a point source is $1.0\times {10}^{-8}W{m}^{-2}$ at a distance of $5.0m$ from the source. What will be the intensity at a distance of $25m$ from the source?

Answer 1

Step 1: Given data:

The intensity of sound from a point source is $I_1=1.0\times {10}^{-8}W{m}^{-2}$

The first distance from the source $r_1=5m$

The second distance from the source $r_2=25m$

Step 2: Formula used:

From intensity square relationship-

We know that the intensity $I\propto \frac{1}{r^2}$

Step 3: Calculate the intensity$I_2$

Using the formula of intensity square relationship

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

Therefore we can write as, and substitute the values

$\frac{I_1}{I_2}=\frac{{r_2}^2}{{r_1}^2}$

$\begin{array}{rcl}{I}_1{r_1}^2& =& I_2{r_2}^2\\ I_2& =& \frac{I_1{r_1}^2}{{r_2}^2}\\ I_2& =& \frac{\left(1\times {10}^{-8}\times 25\right)}{625}\\ I_2& =& 4\times {10}^{-10}W{m}^{-2}\end{array}$

Therefore the intensity is $4\times {10}^{-10}W{m}^{-2}$.