Destructive Interference of two waves

1. Feb 12, 2016

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?
Thanks
SD

2. Feb 12, 2016

Staff: Mentor

It is all KE at that point.

3. Feb 12, 2016

SDewan

4. Feb 12, 2016

Staff: Mentor

"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.

5. Feb 12, 2016

Aniruddha@94

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.

Last edited: Feb 12, 2016
6. Feb 12, 2016

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.

7. Feb 12, 2016

Aniruddha@94

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.