Question

The equation of a spherical progressive wave is :

• A. $y=asin\omega t$
• B. $y=asin(\omega t-kr)$
• C. $y=\frac{a}{\sqrt{2}}sin(\omega t-kr)$
• D. $y=\frac{a}{r}sin(\omega t-kr)$

Answer 1

The correct option is D $y=\frac{a}{r}sin(\omega t-kr)$

For spherical source,
$I=P/A=\frac{P}{4\pi r^2}$

Amplitude is given as, $\Rightarrow A=\sqrt{I}=\sqrt{\frac{P}{4\pi r^2}}$.
Thus, the amplitude A of a spherical wave is inversely proportional to the distance r i.e. $A\propto \frac{1}{r}$, Where r is distance of source from the point of consideration.
Ans: D