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## Homework Statement

Suppose you have two pulses, One is a trough, It's amplitude is 3 cm and the other is a crest and its amplitude is 9 cm. Assuming they have the same wave length when they overlap the energy of the created wave is:

1- 1/16 E

2- 1/4 E

3- E

4- 4E

## Homework Equations

##E## is proportional to ##A^2##

## The Attempt at a Solution

(Assuming the waves have the same characteristics)[/B]

The teacher gave us this question so I had to follow this reasoning to get to the forth answer

Suppose that the first wave has E energy and the combined wave by superposition we get its amplitude to be 6 cm (down) so you get 4E

But this doesn't make sense or at least doesn't conserve energy. Another solution using conservation of energy, the first wave has E and the second has 9E then the total energy would be 10 E

I could apply this to a simple question, Assume both crest and trough have the same amplitude, when they overlap you will get zero amplitude.. Where did the energy go? It has changed its form to become kinetic energy just as in a spring. So the total kinetic energy is 2E

Another situation is when two crests or two troughs overlap, it loses all its kinetic energy and it will only have potential energy. If you use energy conservation you get 2E. But if you use the E proportional to ##A^2## you get 4E.

So my question here, Does that proportional doesn't apply in superposition situation or my thinking is wrong? I couldn't look for the math behind it because it has integration and partial derivatives in the derivation for the energy equation of a wave. I have only studied derivatives so I wish you could somehow support your argument with some math