Ok... So no one bites..?
With audience applause I believe it is mostly the acoustics of the enclosure.
Of all the white noise.., eventually there will likely be a larger number of people clapping at the same time than than they all being equally spaced... That slight grouping will be reflected back to the audience in general... More and more people will pick up on it and tune their applause to it. Adding to the amount of feedback for the rest of them to get into... Of course there are probably other causes.., such as tuning into your neighbors clapping.
With particles, I'll illustrate what I *think* happens. With a steady source of particles. Any uniform variation of the source will of course produce the wave instantly... We do it with rf but it's unlikely in nature... So I'm looking for more than that. And not based on 'time' of course...
There are other perturbations I'm sure but I'm picking one I know.. And I'm trying to keep is simple more for myself than anything else... Cause maybe this is all already all known... And math, etc. confuses the pictures in my head too...

Because this is not spaced text I have to use spaces '-' between particles 'x'.
For particles with mass... Count the -'s...
x-----x-----x-----x-----x-----x-----x-----x-----x-----x| Leading edge.
Because there is no forward gravitational pull to the leading particle it is pulled back to the 2nd particle.
x-----x-----x-----x-----x-----x-----x-----x-----x----x|
With the increased pull of the 1st particle, the 2nd particle moves toward the 1st..
Thereby reducing its gravitational pull on to the 3rd particle.
x-----x-----x-----x-----x-----x-----x-----x------x--x|
This continues so that all particles eventually bunch into the waveform.., or 'packets' of energy.
x-----x-----x-----x-----x-----x-----x----x--------xx|
x-----x-----x-----x-----x----x------x--x--------xx|
x-----x-----x-----x------x--x--------xx--------xx| peaks close 5-4-2-0
x-----x-----x----x--------xx--------xx--------xx| valleys open 5-6-8
x-----x------x--x--------xx--------xx--------xx| for the sake of the example.
x----x--------xx--------xx--------xx--------xx|
-x--x--------xx--------xx--------xx--------xx|
It appears that forming the wave lowers the velocity of the particles, compared to that of a single particle.. Showing my ignorance, and I could look it up too.., but is this a known phenomenon..?
This above shows pretty much a square wave.., but in practice as all the particles shared their relative amounts of gravity.., I'm sure it would come out as a sine.
From there I'd like to know if there are more and more particles being emitted from a source, would it change the frequency or just the energy..? Would it be the mass of the individual particles...?
What brings on a particular wavelength...? Any opinions..?
And what about photons which are said to be weightless... Although they have energy. I'm still not sure how they can form waves at all... But I hear they do.
Thanks...
interesting thread. its spin velocity, and counter spin. It acts as a singularity. it can collapse a magnetic field all at once.. Spherical waves.