In the total destructive interference of a wave, the peak of one wave, perfectly aligns with the trough of another wave (assuming they have the exact same amplitude and phase), causing the waves to cancel out (I know this is very difficult experimentally).

An example using water waves would mean the output is the still surface of water, using sound waves, you would get complete silence, using light, you would get darkened etc.

I have been trying to get my head around the idea of destructive interference causing energies to “destruct”, leaving “nothing” behind but I know this is against the first law of thermodynamics, which means energy cannot be created or destroyed. Have I misunderstood something fundamental?

I’m trying to understand this somewhat philosophically using analogies.