How is sound produced looking from the atomic level? My thought process goes like this: Atoms are not perfect circles/solid spheres which we use to describe many macroscopic/classical phenomena.They have only electrical boundaries.There is also empty space between them. So, if atoms collide/vibrate how would it produce what we perceive as sound?
The wavelength of sound waves in a solid is much greater than the dimensions of atoms. For example the speed of sound in steel is 6100m/sec, so the note middle C (262Hz) has a wavelength of about 23 metres. Sound waves are collective motions of a vast number of atoms, and it isn't especially helpful to think of them as being generated by atom scale phenomena.
Because, as you mention in your question, atoms don't have a sharp edge, in a solid like steel atoms can be pushed together slightly and pulled apart slightly. This gives the solid some elasticity, and this elasticity allows compressions waves (i.e. sound waves) to travel through the solid.
I think you are asking how can we visualize sound being produced from the atomic level to the macroscopic level. So, like you've said, atoms are fuzzy. And it seems like sound can't be produced because atoms are mostly empty space!
Okay, let's take a solid and zoom down to the atomic level. We can imagine a giant lattice of atoms all bound together by the mutual attraction and repulsion of electrons and protons. How atoms bond together is another question by the way.
So each of the atoms are described by probability density functions. Once a disturbance is made and causes a jiggle, i.e. a potential field is applied, the probability density function of the atoms closest to the potential will change in shape. The atom may move up to a higher energy level, (eigen value), with a corresponding quantum state, (eigen state). Keep in mind groups of atoms would be affected at the same time. So now with this new probability density function shape change, it must therefore affect atoms next to it!
The atoms right next to the atoms that just changed quantum states would be experience a new potential field from those very atoms! Again, they will be perturbed, and the pattern continues just like a wave.
So I'm imagining a wave where every atom in the lattice changes in quantum state. This "propagation of quantum state change" continues through the solid object to the air consisting of N2 and O2 molecules, dust particles, etc. This propagation keeps going until it goes inside your ear drum where the same thing happens... and lastly from all those collective interactions, it produces a "sound" that you experience. You can look up how the ear works, That's where biology takes over, but is essentially physics too. :D