0
$\begingroup$

this question has been asked many times and none seem to completely answer or i am unable to understand the answers

So let us consider two mechanical transverse waves traveling in opposite directions on a string let us further consider the moment where they interfere destructively

at the moment when they interfere we see the string as if nothing happened then what happened to energy ? where does it "hide"?

$\endgroup$
1
$\begingroup$

The simple equations of motion for waves on a string provide that a general interference (as of two slightly-different frequencies) will make an energy concentration that is textured at the square of a wave at the difference frequency (which has energy lumps at twice the difference frequency). While that is amusing, it is also the principle that radios traditionally use in mixing a received wave down to an intermediate frequency.

A more complete example of destructive interference is in the antireflection coatings on camera lenses; the partial reflection from one layer may completely destructively interfere with the partial reflection of another layer, so that there is NO reflected light energy. The energy in the incident light therefore is not lost to reflection, only the transmitted light remains (and it is undiminished by any reflection). Thus, the energy is again in a region which is NOT the region that corresponds to destructive interference.

Unless a non-wave-equation term (such as absorption or gain) is present, the wave interference phenomenon distributes energy in a variety of ways, but does not lose it. It's not hiding, it's just... not particle kinetic energy, so is not localized to a particle location.

| cite | improve this answer | |
$\endgroup$
1
$\begingroup$

Well in the case of a mechanical wave (as you described), you cannot freeze the wave in one instant in time and then ask what the energy is, you lose this way the information about the velocity (and hence kinetic energy). The potential energy will be $0$ but the temporal derivative of the wave, which is connected to the velocity (and its square is connected to the kinetic energy) won't be.

This is exactly like a single particle attached to a spring, and asking where the energy is when the particle is at $x=0$, it is in the velocity.

| cite | improve this answer | |
$\endgroup$
  • $\begingroup$ and the velocity is in which direction? $\endgroup$ – user250074 Dec 24 '19 at 9:57
  • $\begingroup$ The direction of the oscillation of the wave. If the wave is oscillating in the y direction, then in the y direction, because that's the direction the particles are moving when the wave passes through them $\endgroup$ – Ofek Gillon Dec 24 '19 at 9:58