MIMF

I am trying to design a pineapple shaped Weissenborn. The grain pattern of the top would look good with 2 sound holes - one on either side of the strings. Is it necessary to have a sound hole directly under the strings, or is this just tradition

Tradition mostly; lots of other things have been done, although they don't seem to catch on. If you can get hold of American Lutherie #1, or the first 'Big Red Book' from the GAL, there's a good article on air resonances by William Allen that has some things to say about soundhole location. I've done some experiments that indicate a relationship between the usual sound hole location and the waisted shape of the box, but on a pineapple uke that's moot.

Moot (in this case) perhaps but intriguing nonetheless. Can you say more about this relationship?

"Can you say more about this relationship?"

Well, it gets complicated....

Start out by thinking of a rigid walled tube, about the same length as a guitar, that is closed at both ends. The lowest resonance will be a lengthwise 'sloshing' mode of the air, at about 350 Hz. There will be large pressure changes (high sound levels) at the two ends of the tube, and the energy will all be in flow in the center, giving a null in the sound. This is often designated the 'A-1' air mode.

Suppose you put a 'waist' in the tube; something that reduces the cross sectional area, with a narrow point a little above the center of the length, where a normal guitar waist would be. The flow through the waist will speed up, and where the flow speeds up the pressure is reduced, so the flow max (and pressure null) will be moved 'north' a bit from the center of the tube. The frequency might be a bit different from that in a plain tube.

Now take a plain straight tube and punch a hole in the side where you'd have a normal sound hole. In this case, since there will be some flow past the hole, it will tend to suck a little bit of air in when the flow is high. This increases the mass of air in the upper end of the tube a little, and pushes the pressure null down a bit. The frequency will probably be lower than the mode in a plain tube.

Now, still working with a rigid tube, put in both the waist and the hole. What will happen is that the two competing effects will balance out in some way, so that there will be one lengthwise sloshing mode, possibly with a different frequency from any that you've seen, and a null that may or may not be displaced from the center of the tube.

So, OK, but the guitar is not a rigid tube. In particular, we know that almost all guitars (unless they're really screwed up) have a 'lengthwise dipole' top resonance. The active area of this mode below the bridge is well placed to 'pump' air along the length of the box, and drive that A-1 mode, AND the long dipole top mode often comes in at around 350 Hz, like the A-1 air mode. Even if the frequencies are not particularly close, these two mode will be strongly coupled, simply by their geometry. Strongly coupled modes yield pairs of resonances that involve both members: you can expect the top and the air both to be moving at both frequencies but, like the 'bass reflex couple', there is likely to be more energy in one or the other at a particular pitch.

In this case, what you'll see is a pair of 'air' modes, one with the null moved 'north' and the other with the null moved 'south', at different pitches. The one that has the 'northern' null will not radiate much sound through the sound hole, because the pressure doesn't change much there. The one with the null moved 'south' can be a very strong radiator of sound, and the SPL in the top of the upper bout will be even higher. You may or may not see a Chladni pattern on the top at or near both pitches: if the top motion and the air pressure are out of phase (top below the bridge moving 'in' as the pressure rises at the tail block) a fair amount of energy could be transferred from the top to the air with little motion of the top; not enough to form a pattern.

Note that this requires:
1) a pronounced waist a little above the center of length of the body,
2) a sound hole a little above that, and
3) a top that can move in a way that drives the air mode.

The first time I saw this was on a classical guitar, where it produced a strong output peak near 440 Hz, where there should not be one according to the literature I'd seen. This peak fell nicely in between the expected 'long dipole' peak at about 350 Hz, and the 'cross tripole' around 500, and so filed in what would have been a 'hole' in the response around the fifth fret on the high E string. Measurements that I made at the time I first saw this (more than ten years ago!) indicate that this sort of mode couple is often missing on Dreadnoughts, which don't have a pronounced waist. Guitars without a 'normal' sound hole (say, one that's been moved up into the upper corner) also lack this couple. A port in the upper bout near the base of the neck will radiate a lot of energy from the A-1 mode, and will alter the relationship and frequencies, at the very least. All of this points up a possible reason why the usual waisted shape, with a soundhole in the top above the waist, is so persistently 'normal' for guitars.

Interesting, thanks for the info. I wish I understood this well enough to apply it in a useful way. I always aprreciate your thorough answers, even though sometimes I end up feeling sorry I asked.

I guess the take home message (for a guy like me) is 'Don't stray too far off the beaten path.'

Interesting indeed, thanks Alan.

I too wish I had a better understanding of how this all works.

Unlike Bryan, I am already so far off "the beaten path" (Deodar cedar for a pineapple Weissenborn) that I might as well continue. I am considering using two sound holes one on either side of the strings but might add an internal baffle to simulate a half-waist just below each one.

All comments welcome

Nice explanation Alan.

I am glad someone like is available to help the rest of us!