Destructive Interference of two waves

[SDewan]

On a single long string, two sinusoidal pulses are started from either end. They have a destructive interference.
Both the pulses have kinetic as well as potential energy. Now the point at which they meet, there being a destructive interference, no crest or trough is formed. But right after that, they seem to have continued their initial respective motions.
My doubt: Where does their energy go at this point? How does it come back right after this point?
Solve my problem, please.
Thanks
SD

 

[Dale]

Where does their energy go at this point?

It is all KE at that point.

 

[SDewan]

Please elucidate

 

[Dale]

"No crest or trough" means that the position of the string is all 0, the equilibrium position. But the string is not at rest, it is moving. Therefore it has KE.

 

[beamie564]

Intuition suggests that the energy is purely kinetic. But to explain this phenomena to myself I took the following view: Consider the point where the two pulses meet to be a fixed end. The pulse coming from the left gets reflected and also inverted, same with the other pulse. So while it appears to us as if the pulses have passed each other unscathed they actually are reflected and inverted.
I don't know how correct this is but it does provide some reasoning.

 

[nasu]

You can imagine that they reflect but this is inconsistent with general reflection behavior. Reflection happens when you have a change in the properties of the medium.
So why would you have reflection in the middle of a homogeneous string? There is no interface or discontinuity there.

 

[beamie564]

You can imagine that they reflect but this is inconsistent with general reflection behavior. Reflection happens when you have a change in the properties of the medium.
So why would you have reflection in the middle of a homogeneous string? There is no interface or discontinuity there.

Yeah I get that.. That's why I said this wouldn't be a rigorous explanation, rather just a helpful way of thinking about it.