Do all impacts create a wave-like disturbance in the medium through which they travel? There is a scene in the first Matrix movie, where a helicopter strikes a skyscraper. The most interesting part is the 'slow-motion' bit where, as the helicopter strikes the building, a wave first propogates from the impact zone, outward along the facade, before the glass finally shatters. I was wondering whether this same thing happens across the board. Is a wave produced every time two surfaces come into contact (AKA collide)? 
This is the clip I'm referring to: https://www.youtube.com/watch?v=2E3JDtqHaVM&t=3m56s
 A: I think it's safe to say yes for all elastic (non-rigid) material.
I believe it depends on the elasticity. Deformation (Strain) occurs in pretty much every body because of the force you apply and it could be temporary at a macroscopic level due to the elasticity.
So an impulse results in a compression wave that propogate through the material.
Deformation also gives raise to the tranverse waves that you see in that clip, as the a compression on one axis affects the dimensions in other axes.
That is, what I believe, results in the wave-like pattern that you are talking about.
The dependent factor is elastic modulus. (Or stiffness: the extensive property)
It becomes permanent and can lead to structural  failure depending on the intensity of the force and nature of the material; specifically the elasticity.
But yes, I think it's safe to say yes, to your question.
Interesting video showing compression waves in a spring: https://www.youtube.com/watch?v=ubRlaCCQfDk
Note: I guess the elasticity in the matrix is different to that of our world, given the extent to why the bodies deform.
A: Yes, when two objects collide, there's some excess pressure in the impact zone but the pressure propagates by the wave equation through the material – it's nothing else than the mechanism by which sound propagates in a medium. Also, waves may be transverse or longitudinal (the variation of the position is going in parallel with the direction of the wave). 
The film focuses on the transverse one which is not the "main part" of the sound wave but it is nonzero, too.
The amplitude of the sound wave is clearly exaggerated in the movie as well (the conventional solid, non-rubber-like materials would break long before they would be this deformed) while the frequency is severely lowered but the principle reflects how Nature works.
