Superposition Of Transverse Waves.

[Shan Ravi]

When two waves traveling in opposite direction say in a thread, superpose the shape of the thread becomes flat. Where is the energy stored in the thread now. When a single is travelling, we say energy is stored as potential energy. But here there is no displacement of the thread in the vertical direction. So, there should be no energy stored. But they emerge out as two different full waves... where did this energy it derived from again?

 

[ZapperZ]

When two waves traveling in opposite direction say in a thread, superpose the shape of the thread becomes flat. Where is the energy stored in the thread now. When a single is travelling, we say energy is stored as potential energy. But here there is no displacement of the thread in the vertical direction. So, there should be no energy stored. But they emerge out as two different full waves... where did this energy it derived from again?

The "energy" here is not just in the displacement of the wave oscillation, but also on the speed that it has. So even when there is a destructive interference, that is occurring only instantaneously for a traveling wave, and that points is still having a velocity, only it has zero displacement from the equilibrium point.

There is a very good and complete treatment of this issue in a AJP paper:

"What happens to energy and momentum when two oppositely-moving wave pulses overlap?", N. Gauthier, Am. J. Phys. v.71, p.787 (2003).

Zz.

 

[Shan Ravi]

But the speed it has also traveling normally (I mean before superposing). So do you mean to say that the speed of the transverse vibration of the particles increases during superposition?

By the way, where can I read the AJP paper?