91Ó°ÊÓ

• Intensity of the wave is$I=1.91×{10}^{−4}{\text{W/m}}^{\text{2}}$
• Radius$r=2.5\text{0m}$

Intensity of the source is given as the rate of energy (power) per unit area. Let, that source be centered at the sphere, having area$\text{4Ï€}{\mathrm{r}}^2$. From this, calculate the power of the source. P is the power of the source, r is the radius of the sphere, and I is the intensity of the source.

The expression for the power is given by,

$P=I×A$

Here is the intensity and A is the area.

To calculate the power of the source,

$P=I×A$

Substitute $1.91×{10}^{−4}{\text{W/m}}^{\text{2}}$for l and$4\mathrm{π}{r}^2$ for A into the above equation,

$P=(1.91×{10}^{−4}{\text{W/m}}^2)×\left(4\mathrm{π}{r}^2\right)$

Substitute for into the above equation,

role="math" localid="1661538919438" $\begin{array}{l}P=(1.91×{10}^{−4})×(4×3.14×{\left(2.5\right)}^2)\\ =1.50×{10}^{−2}\text{W}\end{array}$

Hence, the power of the source is $1.50×{10}^{−2}\text{W}$.