Why does a mechanical wave have a reflection when it hits a boundary?

Question

When a mechanical wave hits a denser or less dense substance, there is a wave reflected. Why does it occur, and why does it not occur when density is constant?

Answer 1

Continuity?

Actually, it is not a matter of density but of any difference in the propagation parameters. For example, if you attached two slinkies of different types together, you'd see a reflected wave coming from the transition.

http://en.wikipedia.org/wiki/Slinky

If you had two pieces of steel with identical densities but different elasticities (spring constants), ditto.

And not just mechanical waves. Light will reflect from a transition between materials of different index of refraction:

http://en.wikipedia.org/wiki/Fresnel_equ...

Surely you've seen reflections in a clear window?

It seems ***-backward and counterintuitive but once you accept that the differential equation that describes the wave motion really is what is going on in the real world, then it follows that whatever happens in the real world must satisfy the differential equation.

And the differential equation says that there will be at least some reflection at any discontinuity. Just how much and what the reflection will look like depends on the nature of the discontinuity.