Phil wrote:
"In a past life, we had everything you'd need to measure this, except for the string strike mechanism, which we could have fabricated."
The hecks of it is, that's the _easy_ part; use the 'wire break' method. Copper magnet wire is almost insanely uniform stuff: it has to be, or they couldn't make it at all. If you loop a short length of something like #43 wire behind a string, and pull on it until the wire breaks, you'll get a 'pluck' that will hardly vary in strength from one time to the next. IIRC, the range of force I got over something like 18 trials was about 4%. It's also easy to control the exact spot you pluck at, and the direction of the initial displacement. What more could you want?
I have done some measurements in a little 'anechoic closet' I built, using a solenoid operated plucker based on the wire break technique. With a half dozen trials of any given string/configuration, you've got reasonably good data to look at. You can also loop the wire under a string _behind_ the saddle, so that you're applying a 'step' force at the bridge. Unlike the 'impulse' of a hammer, this has more energy in the low frequencies, but the difference is easy to characterize and correct for.
I talked over the idea of measuring the 'power' of one of my guitars with my acoustics guru years ago; it's harder than it looks. The sound pressure level, what you measure with a dB meter, gets you part of the way there, but you also need to understand how that level drops off with distance, and also how it varies in different places. And, of course, there's the frequency thing... Still, SPL in a given location at a given distance is a pretty good stand-in for volume, if you can figure out a way to account for the way spectral changes factor in.
Big guitars are more bass balanced, but it's easier to make a loud small guitar than a loud big one. There are two reasons for this: the spectrum of the sound output, and the physics of how the guitar produces sound.
Guitars strings by themselves don't really transfer usable amounts of energy to the air; that's why we tie them to a soundboard. The lighter the soundboard is, and the bigger it is, the more effective it will be, so the overall sound power is related to the ratio of Area/mass. We always try to make soundboards as light as we can, but they need to be stiff enough to hold up under bridge torque. As you increase the span to make a larger soundboard, you have to beef up the structure to keep it stiff enough, and it turns out that, for a given type of structure the mass goes up faster than the area. Thus a small guitar with a given sort of top structure (say, X-bracing), with tend to be more powerful than a larger one.
The soundboard is, of course, a 'speaker', and we all know that larger speakers work better at low frequencies than small ones. A larger box will also have more air volume, and tend to have a stronger 'Helmholtz' resonance in the low range. Thus bigger guitars tend to be more bass balanced. Our ears, though, are more sensitive to higher frequencies, which the more massive larger box may well make less of. Thus a smaller guitar will tend to have a sound that 'carries' better; is audible further away.
It's interesting to speculate at to why big boxes are felt to be 'more powerful' than small ones. I have to wonder if it does not have to do with that fact that big animals that make low pitched sounds are more powerful, and so we associate 'bass' with 'power'. When the little yappy dog barks, you worry about him peeing on your shoe, but when the big dog barks, you back off.
|
