Question

A line source emits a cylindrical expanding wave. If the medium absorbs no energy then the amplitude will vary with distance $r$ from the source as proportional to

• A. $r^{-1}$
• B. $r^{-2}$
• C. $r^{-1/2}$
• D. $r^{1/2}$

Answer 1

Answer: (C)

$r^{-1/2}$

For cylindrical wave intensity at any distance r can be given by $I=\frac{Power}{A_{surface}}=\frac{P}{2\pi rl}$. So the intensity is proportional to $\frac{1}{r}$. Hence the amplitude will vary with r as $A\propto \frac{1}{\sqrt{r}}$
Ans: C