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Let's say the two waves are $y_1=\cos(\omega t-kx)$ and $y_2=\cos(\omega t-kx+\pi)$

Here, $\omega$ is the angular frequency of wave, $k$ is the angular wave number, and $t$ is time.

They destructively interfere to produce no net movement of the medium particles everywhere and at all times.

Both the waves carry certain energy but where does this energy manifests itself after interference? I searched on the internet and found the answer "energy goes somewhere else".

But here there is only destructive interference everywhere and no constructive interference anywhere so in what way is the energy stored in the system?

Nihar Karve
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Bhawna Rana
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  • The energy is always stored in the medium. For sound or water its the elasticity of medium will hold the energy. – PhysicsDave Dec 31 '21 at 21:20
  • better answer here https://physics.stackexchange.com/questions/623648/can-interference-take-place-in-medium-itself/626362#626362 – PhysicsDave Dec 31 '21 at 21:29

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The energy goes back into the sources. In order to get complete interference everywhere the sources must be co-located so any energy lost by one source is immediately gained by the other source.

Dale
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  • What about plane waves? Does conservation of energy apply here? – jensen paull Dec 28 '21 at 14:55
  • Yes, of course. Why wouldn’t it apply? – Dale Dec 28 '21 at 15:50
  • Purely about Em waves: imagine 2 plane waves going in opposite directions, such that they form a standing wave. When they're in phase the energy is non zero. And when they're out of phase the E field is zero. But because they're plane waves there is no source. I can't wrap my head around how energy is conserved – jensen paull Dec 28 '21 at 16:34
  • @jensenpaull Plane waves have sources. The source of a plane wave is an infinite sheet of current. However, for such a standing wave the energy just sloshes back and forth between the nodes. It is always there, but it alternates between electric and magnetic components. See here for a detailed answer about energy flow in a standing wave https://physics.stackexchange.com/questions/602055/energy-propagation-through-stationary-points-of-a-standing-wave/602182#602182 – Dale Dec 28 '21 at 22:59
  • Ah yes, thanks, overlooked the magnetic component. – jensen paull Dec 28 '21 at 23:47
  • The energy is always stored in the medium. For sound or water its the elasticity of medium will hold the energy. – PhysicsDave Dec 31 '21 at 21:20
  • better answer here https://physics.stackexchange.com/questions/623648/can-interference-take-place-in-medium-itself/626362#626362 – PhysicsDave Dec 31 '21 at 21:30