Question

A wave travels uniformly in all directions from a point source in an isotropic medium. The displacement of the medium at any point a distance ${}^{\prime }r{}^{\prime }$ from the source may be represented by ($A$ is a constant representing strength of source)

• A. $\left[A/\sqrt{r}\right]$ sin $(kr-\omega t)$
• B. $\left[A/r\right]$ sin $(kr-\omega t)$
• C. $\left[Ar\right]$ sin $(kr-\omega t)$
• D. $\left[A/r^2\right]$ sin $(kr-\omega t)$

Answer 1

Answer: (B)

$\left[A/r\right]$ sin $(kr-\omega t)$

For a spherical wave(travelling uniformly in all direction from a point source ), the amplitude decreases with distance from the center as $1/r$. As a result the intensity of wave varies as $1/r$.

Hence, the displacement of medium with $r$ goes as $y=\frac{A}{r}sin(kr-\omega t)$