# Why waves in superposition pass through each other without interference in same medium?

Wave can interact constructively (add up) or destructively (cancel) but how about when they are in a superposition state why is there no interference when they meet up in same medium? Imagine 2 pulses of different amplitudes approach and went passed each other in same medium should interfer but it isn't so in superposition as they can pass through each other undisturbed.

• Can you give an example so that I can get to know exactly what you meant? – KV18 Apr 10 '19 at 12:16
• @KV18: edited my question to make it clearer. – user6760 Apr 10 '19 at 12:25
• They do interfere, but they don't interact. – eranreches Apr 10 '19 at 12:28
• What is the difference between interfere and interact? – KV18 Apr 10 '19 at 12:30
• Interference is a term which was introduced many years ago and has not been changed although it possibly gives the wrong idea about the phenomena. One wave does not influence (interfere with) the passage of another wave. – Farcher Apr 10 '19 at 14:12

When the wave equation in the medium is linear, waves will pass right through each other.

A linear differential equation means that when $$\Psi(\vec{r}, t)$$ and $$\Phi(\vec{r}, t)$$ are solutions, then also any linear combination (for example their sum) is a solution.

This is true to good approximation for light and sound in air. • I feel like this sort of begs the question. It's saying "Waves don't interact because they don't interact". – DanielSank Apr 10 '19 at 15:58
• @DanielSank, to be fair, most of physics is that way when you try to dig into it deep enough. – The Photon Apr 10 '19 at 15:59
• @ThePhoton I guess that's kinda true, but when someone asks "why" I figure it means they want to go one level deeper than what they presently understand. – DanielSank Apr 10 '19 at 16:03
• @DanielSank The question was general, so I gave a general answer. I hinted at conditions when it is not true: when the wave equation is not a linear equation. Examples would be stiffness waves, phonons in crystals with anharmonicities, water waves. – Pieter Apr 10 '19 at 18:27
• @Pieter yeah sure whatever. The point is that "linear" means that the response of the medium is independent of it's state. – DanielSank Apr 10 '19 at 22:00