How to Prove AI = AT + AR for Wave Amplitudes?

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SUMMARY

The discussion centers on proving the equation AI = AT + AR, where AI, AT, and AR represent the amplitudes of incident, transmitted, and reflected waves, respectively. The conservation of energy principle, represented by W1 = W2, is crucial for this proof. The wave equations provided, yI(x,t), yR(x,t), and yT(x,t), illustrate the relationships between wave amplitudes and their respective velocities. Understanding how to calculate energy in a wave is essential for validating this equation.

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  • Familiarity with the principle of conservation of energy in physics.
  • Knowledge of amplitude and its significance in wave behavior.
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Aaron8153
I know that:
yI(x,t) = AI sin [k1( x - v1t )]
yR(x,t) = AR sin [k1( x - v1t )]
yT(x,t) = AT sin [k1( x - v2t )]

W1 = W2
k1v1 = k2v2

I am unsure about how to prove that AI = AT + AR
Where AI, AT, and AR are the different amplitudes of the incident, transmitted, and reflected waves.
 
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Basically, it's that "W1 = W2" which, I take it, is "conservation of energy". Do you know how to calculate the energy in a wave?
 

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