Q. The equation for spherical progressive wave is (where $r$ is the distance from the source)
A) $y = a\sin{(\omega t - kx)}$
B) $y = \frac{a}{\sqrt{r}}\sin{(\omega t - kx)}$
C) $y = \frac{a}{2}\sin{(\omega t - kx)}$
D) $y = \frac{a}{r}\sin{(\omega t - kx)}$
Explanation
(d) For spherical wave intensity $(I) \propto \frac{1}{(Distance\ r)^{2}}$
also $I \propto a^{2} \Rightarrow a \propto \frac{a}{r}.$ Hence equation of a spherical wave is $y = \frac{a}{r}\sin{(\omega t - kx)}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.