Question

Spherical waves are emitted from a 1.0 W source in an isotropic non-absorbing medium. What is the wave intensity 1.0 m from the source?

• A. $\frac{1}{3\pi }W/m^2$
• B. $\frac{1}{4\pi }W/m^2$
• C. $\frac{1}{2\pi }W/m^2$
• D. $\frac{\pi }{4}W/m^2$

Answer 1

Answer: (B)

$\frac{1}{4\pi }W/m^2$

If a point source emits wave uniformly in all directions, the energy at a distance r from the source is distributed uniformly on a spherical surface of radius r and area $S=4\pi r^2$. If P is the power emitted by the source, the power per unit area at a distance r from the source is

$I=\frac{P}{4\pi r^2}$

Thus at a distance of 1m the intensity is given as $I=\frac{1}{4\pi \times 1^2}W/m^2=\frac{1}{4\pi }W/m^2$