Reflected Transmitted Energy

For a harmonic wave moving in one dimension, the total energy flux, i.e. the energy flowing across a unit normal area per unit time is given by



In case of a string, the above expression gives the rate at which energy is carried along the string by the travelling wave. Thus, the rate at which energy arrives at the boundary point, x = 0, with the incident waves is



where is the impedance of left string. Similarly, the rates at which energy is carried by reflected and transmitted wave are



Thus, the energy is conserved, and all incident energy is either reflected or transmitted. Further, we find

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