A mass that has velocity and a force f1, can create a sound and even break a wall upon impact. However if the same force f1 is applied to the wall without any motion (velocity) then the wall will not break and no sound can be heard. Why is this? I suspect that since the mass is in motion it is traveling as a wave and upon impact this wave is what generates a vibration and sound. I also suspect that the vibration caused by this impact causes the molecules around the impact area to vibrate at its harmonic frequency (causing the molecules to break apart). Is any of this true? Or am I off base? What equations exists that describes the vibrations upon impact?? Thanks!!
One does not need to call on the wave nature of matter to explain this. Most of a perfectly good classical answer is:
What equations exist? To my knowledge, problems of this kind are dealt with practically (and very dryly) by engineering rules of thumb and engineering standards specifying impact tests (Charpy test and so forth). For a more mathematical treatment: hopefully you'll also get an answer from someone who studies this kind of acoustics or who analyses the effect of explosives. These are the kinds of people I would go to first to try to get an answer.