If two sinusoidal waves that are out of phase and moving in same direction interferes then how will energy be distributed?

Question

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?

Answer 1

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.