mass loading top

[jahuntle]

I'm watching the Luthier Academy Guitar Analysis and Testing by Trevor Gore (not sure if you'll see this Trevor, if so, hi!). In the 2nd chapter "Testing", trevor finds the cross dipole chladni pattern at around 279 hz. He then adds a small amount of mass (putty) to the center of the two modes and retests and the same pattern now develops at 274 hz.

I'm brand new to chladni pattern testing, but I had been under the impression that we generally reduce a guitar's resonant frequency by reducing stiffness (scalloping braces for instance). I don't understand how adding mass also lowers resonant frequency. In my novice mind, I would have thought that adding mass would lead to less movement of the top which I would think would have the same effect as making the top more stiff and resulting in a higher resonant frequency.

So my question is does scalloping braces reduce resonant frequency since it reduces stiffness and/or does the reduction in brace mass from scalloping have some offsetting effect on the resonant frequency?

Thanks,
James

ps apologies for asking this before I completed the Luthier Academy course. The question may be addressed in a subsequent lesson.

[johnparchem]

More mass make it harder to move the top, thus slowing down its response. Adding mass does not increase stiffness on its own. Lowering braces reduces mass but by a larger factor reduce stiffness. Change in mass is a linear effect where change in braces height or top thickness is a cubed effect. The intuitive thought you had was a thicker top thus more mass but that also increased stiffness. Mass linear stiffness cube of the difference. Stiffness wins in this case.

In the example you talked about, he probably made a small change in mass but on the anti node thus having a very targeted effect.

[Trevor Gore]

To reduce a resonant frequency you can add mass or reduce stiffness
To raise a resonant frequency you can add stiffness or reduce mass

The mass of a brace is proportional to its height
The stiffness of a beam (brace) is proportional to its height cubed (i.e double the height it is 8 times stiffer in bending)

So scalloping the braces (reducing height) removes stiffness much faster than it removes mass, so a resonant frequency will reduce, but it is harder to add back stiffness than to add mass.

The resonant frequency is proportional to SQRT(stiffness/mass); the monopole mobility (a measure of responsiveness) is proportional to 1/(SQRT(stiffness x mass))

So to make a responsive guitar you have to get the frequencies right with the lowest mass and stiffness. All explained in detail with the appropriate equations properly typeset in the books, of course.