5.1 Power $(P)$

2.1 Transverse waves
2.2 Longitudinal waves
2.3 Differences between transverse and longitudinal waves

3.1 General equation of wave motion
3.2 Wave function
3.3 Equation of a plane progressive harmonic wave
3.4 Important relations

4.1 Speed of different types of wave

5.1 Power $(P)$
5.2 Intensity $(I)$

Power is defined as the instantaneous rate at which the energy is transferred. It is denoted by the symbol $P$.

Let a wave is travelling with a speed $v$. If $s$ be the area of cross-section of the string.

Then in time $t$ volume of the length is equal to $svt$

Total energy transmitted is given by, $$\begin{equation} \begin{aligned} {\text{Total}}\;{\text{energy = (Energy}}\;{\text{density)(Volume)}} \\ E{\text{ = }}\frac{1}{2}\rho {\omega ^2}{A^2}svt \\\end{aligned} \end{equation} $$ Therefore, $$\begin{equation} \begin{aligned} {\text{Power}}\;{\text{ = }}\frac{{{\text{Total}}\;{\text{energy}}}}{{{\text{time}}}} \\ P = \frac{{\frac{1}{2}\rho {\omega ^2}{A^2}svt}}{t} \\ P = \frac{1}{2}\rho {\omega ^2}{A^2}sv \\\end{aligned} \end{equation} $$