Question

A line source emits a cylindrical expanding wave. Assuming the medium absorbs no energy, find how the amplitude and intensity of the wave depends on the distance from the source?

• A. $A\propto \frac{1}{r},l\propto \frac{1}{r}$
• B. $A\propto \frac{1}{\sqrt{r}},l\propto \frac{1}{r}$
• C. $A\propto \frac{1}{\sqrt{r}},l\propto \frac{1}{\sqrt{r}}$
• D. $A\propto r,l\propto \frac{1}{r}$

Answer 1

The correct option is B $A\propto \frac{1}{\sqrt{r}},l\propto \frac{1}{r}$

The intensity of a wave emitted from a line source is given by ,

$I=P/a$ ,

or $I\propto 1/a$ ,

where $P=$ power of source ,

$a=$ area of cylinder of radius $r$ ,

now area of cylinder , $a=2\pi rh$ , (h=height of cylinder) ,

therefore intensity of wave ,

$I\propto 1/2\pi rh$ ,

or $I\propto 1/r$ ...........eq1 ,

we have , $I\propto A^2$ ($A=$ amplitude)................eq2 ,

by combining eq1 and eq2 ,

we get , $A^2\propto 1/r$ ,

or $A\propto 1/\sqrt{r}$