Among the following equations, which one represents the spherical progressive wave? [UP CPMT 2012]
Among the following equations, which one represents the spherical progressive wave? [UP CPMT 2012]
$y = r \sin \omega t$
$y = \frac{a}{r} \sin (\omega t - kx)$
$y = \frac{a}{\sqrt{r}} \sin (\omega t - kx)$
$y = \sqrt{\frac{a}{r}} \sin (\omega t - kx)$
Solution
Intensity of spherical wave, $I \propto \frac{1}{r^2}$
Also, $I \propto a^2$
$\therefore a \propto \frac{1}{r}$
$\therefore$ The spherical progressive wave can be represented as
$y = \frac{1}{r} \sin (\omega t - kx)$
Among the given options, $y = \frac{a}{r} \sin (\omega t - kx)$ is correct.