Tuesday, 21 October 2008

There's no such thing as a free anything

It's easy to destroy everything in the universe. Every student learning acoustics begins by doing so, and they do so with four simple words: "consider a free field". Actually they don't destroy everything, they leave the air, or some other compressible fluid, in fact they fill the newly denuded universe with it which, for all I know, might even leave the universe ahead on the deal. Electromagnetics students get to destroy everything.

Anyway, there's nothing left, apart from maybe a source at the origin, which is a pity for those long enough in the tooth to remember when the old place really looked like something, but it does make the equations considerably easier. That's because now there are no reflections, so energy leaving the source is guaranteed not to come back, and a host of other simplifications. A free field is so useful that we often go to great lengths to create a physical approximation to part of one by building (or hiring) an anechoic chamber.
This is ISVR's large anechoic chamber and it's a lot more impressive when you're standing in it. But it's still an approximation, albeit a close and useful one. A truly free field does not exist.

Economists also have a useful simplification, called a free market. You don't have to bulldoze the universe to make one, but you do have to ensure that all prices are set by mutual consent with no monopolies or cartels and a few other things. No real market behaves exactly like this, though many are close enough to make it a reasonable starting point.

Here's the thing: I don't know any acousticians who believe that free field solutions are inherently better than others and should be pursued before all alternatives. As it happens, non free field problems can often be solved by using a free field Green's function and the appropriate boundary conditions but that still isn't necessarily the best way to do it. I'm just saying.

I'm aware that I've drawn a far from perfect analogy. Sometime I'll discuss whether a perfect analogy is useful - in acoustics at least.

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