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

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.