Equation 1.7-1

[Craig Bumgarner]

Hi, Trying to understand effective mass as it applies to the top's Monopole Mobility. In my most recent guitar, I ran the equation on the top while glued to the sides and clamped in the side mold, no back. Once the back was on, ran the same, not clamped in the mold. Other than the back and removal of the mold, there were no changes to the body. Here are the results*:

You can see the main change is in the peak resonance and subsequently the MM. I suspect the mold and clamp (two turnbuckle clamps pushing sides into the mold) are "mass loading" the sides and increasing the area of the top the is "effective". When the mass is removed, the effective area shrinks, increasing the frequency and the calculated effective mass. If the effective area shrinks, wouldn't this have a negative effect on volume even though it drives the MM number up. I thought MM correlated to volume or at least responsiveness, but to exaggerate, if my EA is only a couple square inches, there won't be much of either.

I'm having a hard time of visualizing what "effective mass" actually is in a guitar. Is it a real thing, or the result of a calculation. Is is the mass that actually produces sound? At 30-40 grams, this is only 5% - 10% of the mass of the assembled top. Is that really all the mass the affects the output of sound? Obviously, I don't have a very good handle on this.

* I know these MM numbers are high for flat top guitars, and even for the Selmer guitars I have tested. MM will come down with a neck, bridge and finish. From limited past experience, I would expect to it to come down to ~ 24. The best of these guitars seem to end up around 18-21 MM, so I may have overshot.

[Craig Bumgarner]

Maybe another way of asking this is whether effective mass equates to effective area (of sound board) somehow and if nothing else changes, if effective mass goes down, has the effective area reduced as well? Effective mass going down sounds like a good thing, but effective area going down does not. ????

[Craig Bumgarner]

One more.... Given the vagaries of whether a top is coupled to the back and phase cancellation method of "uncoupling" the top from the back, does simply dampening the back by holding it against my chest as I tap the top, (along with plugging the soundhole) insure the top is uncoupled? Maybe this introduces errors of its own like mass loading the back.

[Trevor Gore]

Effective mass is a calculate figure that is representative of the amount of top (or back) that is moving and therefore radiating sound.

I think most of your conundrum can be explained by the fact that for a given force, less mass accelerates more and radiated sound level is proportional to acceleration.

Measuring guitar resonances whilst it is in a mould is how I discovered the mass loaded sides effect. As I see it, the benefit of measuring MM whilst the guitar is in a mould depends on whether you can find a relationship between that and how it performs out of the mould. I've never looked at that.

A quick look at my numbers indicates that effective mass is around 30% of the total top mass. There's a lot of mass in the upper bout, which doesn't vibrate very much. If you consider the area inside the node line of of a monopole Chladni pattern I'd say effective mass is comparable to that the mass of that area. Remember, it is called monopole mobility.

One more.... Given the vagaries of whether a top is coupled to the back and phase cancellation method of "uncoupling" the top from the back, does simply dampening the back by holding it against my chest as I tap the top, (along with plugging the sound hole) insure the top is uncoupled? Maybe this introduces errors of its own like mass loading the back.

Damping the back, in my experience, produces only that, i.e. damping. It doesn't seem to alter the coupling. An example of that is that I found that for additional side mass to "work", it has to be bolted in really tightly. If there is any relative movement between the mass and the sides you don't get the intended effect.

[Craig Bumgarner]

Thanks Trevor, this is all very helpful. Am I correct to think the effective area is every bit as important as the mass of that area. That is, for equal effective mass, a larger effective area will radiate more sound, yes? Is Chladni testing the only means of quantifying the effective area independent of effective mass?

[Trevor Gore]

I think it was Prof Jurgen Meyer who came up with the relationship that radiated sound is proportional to (amongst other things) a/m, where a is the effective area and m the effective mass of a mode. Wright discusses this relationship at length in his thesis. As Wright used a 3DOF model, his effective masses seem to bear little relationship to real masses. On the other hand, at least for the monopole modes, the 4DOF model gives much more realistic equivalent masses.

That is, for equal effective mass, a larger effective area will radiate more sound, yes?

Yes.

Is Chladni testing the only means of quantifying the effective area independent of effective mass?

Well, one could probably do it using laser holographic interferometry, but for those of us without a dedicated physics lab, the tea leaves will give a good indication. Just remember that the T(1,1)2 is effectively a concentric dipole.

[kiwigeo]

Mmm...dedicated physics lab

[Craig Bumgarner]

Okay, next stop Chladniville. It seems worthwhile to figure out the area to mass ratio, at least visually if not mathematically.

I have yet to get a working Chladni setup going. My latest effort is not producing enough volume to excite the tea leaks. I'm putting out 98 dB, but tea leaves just sit there. I posted in more detail here:

viewtopic.php?f=33&t=5639

[Trevor Gore]

I've no idea how many dBs my system puts out, but I use 15watts RMS into a 4" speaker (in a baffle) and don't have any problems producing Chladni patterns on a flattop. I do need to use ear defenders, though. A bit more detail here. Make sure you excite (i.e. hold the speaker) on what you think is going to be an anti-node and hold it pretty close to the woodwork (~2mm). Usually you can excite a resonance from a lot further back than that. My sig gen is analogue, so I can get smooth incrementation of frequency. If you are using digital incrementation, lack of resolution may be part of the problem.