Acoustic waves - factors determining their form

[bartekac]

Hi,

I am not a native English Speaker, so some words might not be appropriately used below, but I will try my best to explain what I was thinking about.
In general, I have never learned how acoustic waves emerge microscopically. The application of the theoretical knowledge I acquired was always connected to problems where an acoustic wave was already created and I had to use given properties or quantities to solve them. But I have never come across problems regarding the creation of an acoustic wave itself.
Following the common sense I could say that when e.g. two surfaces collide with each other there is a momentary change in pressure between them which creates an acoustic wave that propagates between the two surfaces and bounces off from them variably. The impact also causes the surfaces to vibrate in their resonance frequencies with amplitudes proportional to the forces exerted on them during the collision. This creates another acoustic waves propagating in the surrounding medium. All of this would result in a certain approximated net wave spectrum, which could be described mathematically.
If that thinking is correct (of course not surely though), then what quantities principally influence the acoutic wave outcome? It would certainly be the ones like the medium properties and certain material coefficients, but what exactly?
This is what I was really intensively thinking about for the last couple of days and there is actually one question that bothers me most:
Is there any way to formulate an overall acoustic wave equation created by two colliding surfaces, when there are given: the momenta of the bodies or the forces exerted during the impact, the area of collision, the shape and material properties of the bodies, the properties of the medium the wave would propagate in?
I would be really grateful if somebody joined me in solving just a part of this problem (the whole thing is probably too complex) :)

 

[voko]

When two bodies collide, I can think of two sources of sound. One of them is aerodynamic, caused by the motion of the bodies in the air. Another is vibration of the bodies during and after the impact. Both sources are difficult to model analytically.

 

[bartekac]

voko, thanks for clarification.
My first post was kind of introductory. I am currently working on a group project connected to game/simulation engines. We want to develop a system of soundmaps, that will be capable of real-time generation of sounds based on the quantities I gave in the bold question. We have already calculated that it might be possible when it comes to today's commonplace PC computational power, because their resolution would probably not exceed values around 64x64.

Generally, the soundmaps are supposed to be represented graphically by images consisting of a number of pixels specified by the resolution. The RGB and alpha values of them will be used to indicate material properties of a soundmap-wrapped body at an adequate location. When a collision between such bodies occur, the corresponding soundmap and physical collision data (forces etc.) is processed in order to calculate a discrete acoustic wave spectrum. The computed information is then interpreted and played by the engine sound component.
Of course it doesn't have to be a thorough analysis, but only something that would result in sounds comparable to the real-life ones.

 

[anorlunda]

It sounds like a difficult problem. You mention shape and materials. Think, for example, of a bell versus a pillow as colliding objects; not to mention nonlinear objects such as a cat or a bottle of nitro glycerine.

There are an infinite number of combinations of shapes and materials. I find it hard to imagine defining simple parameters that describe those shape-material combinations. But for game purposes you could predefined a finite number of sounds, say 1024 sounds. Then assign each object in the game one of those sounds. It is not physics, but it might satisfy the game players.

But I applaud game developers who try to find physical first principles to use in their models. It should be encouraged, even if it can not succeed in all cases.

 

[bartekac]

I wanted to omit the direct influence of shapes on the output sound for now - maybe I will try to do something about it in the future. I mean for the complexity reasons, the sound would be the same if you hit a wooden table with a silver sword and with a silver spoon. Applying only material properties to the system would already be a huge success :)

But for game purposes you could predefined a finite number of sounds, say 1024 sounds.

This was mainly why I started this project - to get rid of the necessity of pre-recording hundreds of sound samples. Only the biggest game development companies have time, proper equipment and software for that.The sound setup with soundmaps would be utopianly limited to creating proper soundmaps for certain materials/objects.
The universal pixel-pixel interaction on colliding surfaces with the maps would include:
1. Getting the RGB and alpha values of the colliding pixels from the first surface
2. Converting the values to certain coefficients describing the material in the place of collision.
3. The same for the second surface
4. Calculating the vibrations of the bodies due to the impact
5. Getting properties of a surrounding medium
6. Computing net acoustic wave output.
Points 2 and 4 are the problems that are, as you already said, very difficult to implement in any way. Maybe if I recorded multiple collsions of certain materials and analyze the acoustic spectra, I could find some relations.

 

[anorlunda]

But shape may have stronger connection to reality than material. Silver, bronze, and steel bells may have nearly identical sounds when struck, but a silver bell and a silver candlestick may sound very different.

Think also of the wide variety of sounds that you can make by striking water in different circumstances.

I suspect complexity is the reality.

 

[bartekac]

You are right, the shape influences the sound strongly, but I meant that the project will be for a long time in a prototype state. So basically - not everything at once, firstly I would do something with materials, because it should be a bit easier.

I suspect complexity is the reality.

Indeed it is, but I believe that the complexity in computation is determined strongly by iteration. At first I would try with a single-pixel soundmap colliding with another and create a discrete spectrum with trial-and-error method. This could lead to something, but it also could not :)

 

[schlukhash]

You may be able to generalise certain aspects. Like..
- every sound is "noise"
- the amount of noise has a certain energy.
- in general metalic objects like swords have a high tendency to resonate very much, because the material is very stiff.
So at a small number of resonant frequencies the energy travels very well, you can build this by having a very steep filter at a few places.
In reality this static model sounds more like a bell, so you need to add deflection and deflection to that.
- a spunge like object absorbs most of the energy so is a similar filter array but with very shallow non resonant filters. Not able to carry the initial impulse very far.
Ofcourse one needs a room to do this in which are a lot of delay lines or convolution model.

So in my honest opinion having done some sound programming I think it may get you up to 15-20% of your cpu power, on a fast machine. Getting a real average sounding model from it. So my mode of thinking would be to play the sounds as samples through a reverb or room/distance model. For a generally better sounding and computationally less expensive solution. Would you have infinite time to do so, it may be cool if you succeed in doing so one day..