Question

The average power transmitted through a given point on a string supporting a sine wave is $0.40$ watt when the amplitude of wave is $2mm$. What average power will be transmitted through this point if its amplitude is increased to $4mm$?

Answer 1

The average power transmitted through a given point on a string is:

$P=2{\pi }^2{f}^2{A}^{2}rSV$

$P\propto A^2$

$\therefore \frac{P_1}{{A_1}^2}=\frac{P_2}{{A_2}^2}$

$\Rightarrow \frac{P_1}{P_2}=(\frac{A_1}{A_2}{)}^2$

$\Rightarrow \frac{0.4}{P_2}=\left(\frac{2}{4}\right)$

$\Rightarrow P_2=\frac{0.4\times 16}{4}$

$\Rightarrow P_2=1.6$

The average power will be transmitted through this point if its amplitude is increased to $4mm$ is $1.6watt$