Question

A ripple is created in water. The amplitude at a distance of 5 cm from the point where the sound ripple was created is 4 cm. Ignoring damping, what will be the amplitude at the distance of 10 cm.

• A. $\sqrt{16}cm$
• B. $\sqrt{8}cm$
• C. $\sqrt{4}cm$
• D. $\sqrt{2}cm$

Answer 1

Answer: (B)

Spherical waves are created in water.

Energy of wave at distance $r$ $E_r\propto \frac{1}{r}$

But $E_r\propto A_r^2$

where $A_r$ is the amplitude of wave

$⟹$ $A_r\propto \frac{1}{\sqrt{r}}$

Given : $A_5=4$ cm $r_1=5$cm $r_2=10$cm

$⟹$ $A_{10}=\sqrt{\frac{r_1}{r_2}}{A}_5=\sqrt{\frac{5}{10}}\times 4=\sqrt{8}$ cm