Q. From a point source, if amplitude of waves at a distance r is A, its amplitude at a distance $2r$ will be
A) $A$
B) 2$A$
C) $A/2$
D) $A/4$
Explanation
(c) Intensity=energy/sec/area=power/area.
From a point source, energy spreads over the surface of a sphere of radius$r$.
Intensity =$\frac{P}{A} = \frac{P}{4\pi r^{2}} \propto \frac{1}{r^{2}}$
But $Intensity = (Amplitude)^{2}$
$\therefore(Amplitude)^{2} \propto \frac{1}{r^{2}}\ or\ Amplitude \propto \frac{1}{r}$
At distance $2r$,amplitude becomes $A/2$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.