Energy conservation in interference phenomenon

[anjor]

If on a taut string, we have a wave pulse traveling in the positive x direction with an amplitude A... simultaneously, from the other end we have a wave pulse traveling in the negative x direction with amplitude -A (i.e., it is faced downwards)
At a certain time t, they will superimpose upon each other, and if we take a photograph at that time, we will see a straight string, with no wave pulses in it.
What has happened to the energy of the two wave pulses? where did it go?

 

[Cyrus]

Where does energy go when you compress a spring? Does it magically disappear?

 

[Andrew Mason]

If on a taut string, we have a wave pulse traveling in the positive x direction with an amplitude A... simultaneously, from the other end we have a wave pulse traveling in the negative x direction with amplitude -A (i.e., it is faced downwards)
At a certain time t, they will superimpose upon each other, and if we take a photograph at that time, we will see a straight string, with no wave pulses in it.
What has happened to the energy of the two wave pulses? where did it go?

Be careful! When the string is flat (no amplitude) is it stopped? Are you saying it has no energy because it has no amplitude?

AM

 

[anjor]

when the string is compressed, the energy is stored as the potential energy of the string.
Andrew,
i know... rather feel that there is something wrong in that statement, however i am not being able to explain it mathematically... could you please elaborate? The only force acting in this system is tension... the energy is stored as the potential energy of "tension"? then.. is the tension in the flat portion of the string different?

 

[nrqed]

when the string is compressed, the energy is stored as the potential energy of the string.
Andrew,
i know... rather feel that there is something wrong in that statement, however i am not being able to explain it mathematically... could you please elaborate? The only force acting in this system is tension... the energy is stored as the potential energy of "tension"? then.. is the tension in the flat portion of the string different?

The better analogy is to consider a mass attached to an oscillating spring at the instant it is at the equilibrium position. The spring is not compressed nor stretched so it doesn't store any potential energy. Where is the energy? The answer if obvious, right? The mass has (maximum) kinetic energy at that instant. The same thing with the string.
I am pretty confident this is what Andrew Mason had in mind with his comment.

Patrick

Patrick

 

[ZapperZ]

There is a terrific article in AJP a couple of years ago on this issue. You may want to look at it.

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

Don't miss the followup comment by D. Rowland that corrected the treatment on longitudinal wave.

D.R. Rowland, Am. J. Phys. v.72, p.1425 (2004).

Zz.