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Ive just been reading some interesting articles on 'tap tuning', a somewhat mysterious art using your knuckles to tap on a soundboard, listening for its quality of tone.

I wonder if anyone does this with a tuning fork instead, striking the fork and holding it against whatever material being tested.

Seems like it would give you more to listen for over a longer duration, and would be closer to what happens when a metal string vibrates against a static focal point connected to the board.

Im not testing soundboards but I have been experimenting with several different materials.

For example, if you take a similiar volume of very heavy bubinga, and very light cedar, their tuning fork tones will be very different. The bubinga will resonate at a much lower volume, and I wonder if there is a general rule to be learned here.

If there are three basic qualities of resonance - volume, velocity and frequency...would it be fair to say that higher density woods will always resonate at a lower volume than lower density woods???

Because the higher mass resists vibration?

Would it be fair to say that higher density woods will dampen high frequencies less than lower density wooods???

Or is it more complicated than that?

The 'resonant frequency' of an object is just the pitch at which you get the most bang for your buck, so to speak. You put in a certain amount of power or force at a particular pitch and get a large amplitude of vibration out. The actual pitch of the resonance is determined by the mass and stiffness/tension of the thing: heavy strings at the same tension give a lower pitch, and so on. But vibrating objects don't just respond at those resonant pitches; they can be driven over a more or less wide frequency band.

The mass and stiffness get into the act there, too. It's intuitively obvious that it's easier to vibrate something light, like a banjo top, at any pitch than it is something heavier, like a guitar top, even if they both have the same resonant pitch. Adding mass makes it harder to move things at high frequencies, but not so much at low ones. Adding stiffness or tension makes it harder to move them at low frequencies, but less so at high ones. But there's another thing that really makes a difference, and that's the 'damping factor'.

Damping refers to the amount of energy that's 'lost' as the thing vibrates. It's not really lost, of course, you can't 'lose' energy unless you convert it to mass, but it's dissipated, as heat, usually, or sound if you're lucky. Damping makes it harder to vibrate things at all frequencies.

Now, you'll note that mass and stiffness/tension tend to have opposite effects in terms of frequencies. We call the effect of mass or stiffness or damping a 'reactance', because it reacts back on the thing we're trying to vibrate, and changes the effect of the force we're applying. At a low frequency the mass reactance hardly matters, and the stiffness reactance is high. As you go up, the mass reactance rises, and the stiffness reactance falls. At some point, the stiffness reactance gets so low that it actually cancels the mass reactance: there's as much energy stored in the spring when it's fully displaced as there is in the inertia of the mass when it's moving it's fastest. All you have to do to keep things going is replace the energy 'lost' to damping.

If you look at the resonance peak of something like a tuning fork, that has really low damping, you'll see that it is very sharply defined. It only vibrates at one pitch, and that's what makes it useful for tuning. Things that have higher damping, like cardboard, have broad resonance peaks. When you tap them, the sound dies away fast, and they don't give a clear impression of pitch. The shape of the resonance peak, then, is a measure of how much damping the thing has. A tall narrow peak says low damping, and a low, wide one implies high 'losses'.

Think of pushing a kid on a swing. If you're going to get them really high up you have to pust at just the right frequency. The same goes for any resonant object. In order for that tuning fork to work well it has to match the natural resonant pitch of the object. However, it can drive the thing some off resonance, and the lighter and less 'lossy' the thing is, the more you're likely to hear. both of your planks are probably well off the pitch of your tuning fork, but the cedar one, being lighter, responds more. If you hit the exact resonant pitch of the bubinga it might give the cedar a run for it's money, as it should have low losses, and could really build up a lot of amplitude over time. Then again, cedar's got pretty low damping, too, and at it's own pitch it can really wail.

So, in order to characterize the way a guitar top vibrates with tuning forks, you'll need a heck of a lot of them, at a lot of different pitches. These days there are easier ways to do it. One way is to use an electronic signal generator to make any pitch tone you want, and drive the top with that. You can listen for the output peaks, or use something like glitter sprinkled around the top that will bounce off moving areas to make the resonances visible. Another way is to get a computer program like 'Wavesurfer', mentioned in the thread on acoustics, and use that to analyse the 'tap tones' by telling you how much energy there is at any given frequency. I'll warn you that this stuff is time consuming and extremely addictive if you're not careful.

Excellent post there Alan, thanks. I have a few questions about it, but I need to study it further first.

Im reading some good articles on the fundamental physics of sound...some of which were linked from this forum.

[QUOTE=Alan Carruth]
Adding mass makes it harder to move things at high frequencies, but not so much at low ones. Adding stiffness or tension makes it harder to move them at low frequencies, but less so at high ones.[/QUOTE]
Ok, lets just consider this part relative to guitar necks...which is what Im obsessed with at the moment.

Prior to 1967 Martin used a very heavy square 3/8" x 3/8" steel truss rod. It was not adjustable and wasnt suspended inside a hollow space, it was imbedded/glued in the neck.

This of course would make the neck a lot heavier than no rod at all, just solid mahogany.

But supposing for the sake of conjecture that there was no rod...how would this change the tone?

Would this lighter neck make the guitar sound slightly brighter...louder???

Telfer asked:
"But supposing for the sake of conjecture that there was no rod...how would this change the tone?

Would this lighter neck make the guitar sound slightly brighter...louder???"

What matters in this case seems to be the ratio of stiffness to mass of the neck. There's a resonant mode of the entire body-neck system that can effect the timbre, particularly in the low range, if it happens to fall exactly on the pitch of the 'main air' resonance. The neck is the most flexible part of the system, and its properties tend to dominate that mode. When you get the match, the tone is usually heard as 'darker' and 'fuller'.

The square tube reinforcement added a lot of stiffness, as well as weight. I don't know what effect removing it would have on the 'neck mode' pitch. I do know that eliminating it would probably allow the neck to pull up too much over time, since there would be nothing to resist the cold creep of the wood. It's there more for playability than acoustics, but, of course, it effects the tone as well.

Well I guess I'll find out in the next few months. The walnut neck Im almost finished has a heavy steel rod, but Im going to make an identical one with an ebony lamination as well.

We'll see if the difference in weight makes a difference in tone.