Question

From a point source, if the amplitude of waves at a distance$r$ is $A$, its amplitude at a distance$2r$ will be

• A. $A$
• B. $2A$
• C. $\frac{A}{2}$
• D. $\frac{A}{4}$

Answer 1

The correct option is C

$\frac{A}{2}$

Step 1. Given data

Amplitude is $A_r=A$ at a distance $r$

Step 2. Finding amplitude $A_{2r}$ at a distance $2r$

$$\begin{gathered} intensity=\frac{power}{area}=\frac{P}{4\pi r^2} \\ intensity\propto \frac{1}{r^2} \end{gathered}$$

Also,

$$\begin{gathered} intensity\propto {\left(Amplitude\right)}^2 \\ \Rightarrow Amplitude\propto \frac{1}{r} \\ \frac{A_r}{r}=\frac{A_{2r}}{2r} \end{gathered}$$

$A_{2r}=2A$

Hence, option C is correct