4.5 Energy in a stationary wave

1.1 Principle of superposition

2.1 Relation between phase difference $\left( \phi \right)$ and path difference $\left( {\Delta x} \right)$
2.2 Interference of waves from coherent sources
2.3 Interference of waves from incoherent sources
2.4 Reflection and transmission of a wave
2.5 Motion of wave during reflection
2.6 Expression for the reflection and transmission of wave

3.1 Transverse stationary wave on a stretched string
3.2 Vibrations in a stretched string
3.3 Melde's Experient
3.4 Resonance

4.1 Open organ pipe
4.2 Closed organ pipe
4.3 End correction
4.4 Resonance tube
4.5 Energy in a stationary wave

The mechanical energy of a wave on a string or in an organ pipe is the sum of kinetic energy $(K)$ and potential energy $(U)$.

At every instant, the total mechanical energy remains constant. However, the energy in a stationary wave oscillates between kinetic energy and potential energy.

Equation of stationary wave is, $$\begin{equation} \begin{aligned} y = 2A\sin kx\cos \omega t \\ \Delta P = 2{\left( {\Delta P} \right)_{\max }}\sin kx\cos \omega t \\\end{aligned} \end{equation} $$

Figure shown below illustrates the exchange of energy over one complete cycle.