Physics of bridges, tops and soundholes

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Rob Dick
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Physics of bridges, tops and soundholes

Post by Rob Dick »

The discussions of various ukes here has got me thinking about the different types of bridge and how that affects the physics of the top and hence the sound. Most mandos have a floating bridge so the strings push the top down, although the Ovation mando has an acoustic guitar style of bridge. The traditional uke bridge tries to pull the itself up and towards the headstock, but the Tahitian uke is more of the mando setup, and it has the soundhole at the back of the body rather than on the top.

I've been building solidbody instruments for a while now but I'm only just delving into acoustic builds. Are there any good books or articles that describe the practical physics of acoustic instruments?
Rob

Owen Woods
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Re: Physics of bridges, tops and soundholes

Post by Owen Woods »

Benade's "Fundamentals of Musical Acoustics" will give you a good overview of vibration and acoustics for musical instruments and is pitched at mathematically minded musicians, rather than musically minded mathematicians. However, looking at the index of my copy, it doesn't have a huge amount of practical information specific to making. If anyone does know of a practical book on this kind of thing then I would be interested as well!

Rob Dick
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Re: Physics of bridges, tops and soundholes

Post by Rob Dick »

Thanks Owen. It's things like the effects of the rigidity or sound absorption properties of backs and sides, the concept of "driving" the top and how it's affected by various bracing and bridge designs, how and why soundholes work etc. that I want to get my head around.
Rob

Chris Reed
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Re: Physics of bridges, tops and soundholes

Post by Chris Reed »

I think there are between 2 and 4 types of bridge.

1. Mandolin type, where the string is fixed at the tail and pumps the bridge up and down.

2. Uke type, where the bridge/saddle combo act as a level at the end of the string, largely vibrating back and forth rather than up and down.

3. (possibly) a combination of these two - i have a cavaquinho with a moustache bridge glued to the soundboard, through which the strings thread, but a floating saddle which sits 1cm or so in front. I'd guess this does a bit of both.

4. (possibly) the violin bridge, whose workings in combination with the soundpost are a mystery to me.

I only know of ukuleles, and on these the mandolin-type bridge generally produces a thin sound and low volume (compare a Tahitian uke to a Hawaiian uke). Of course, making a large-bodied uke with an arch top can produce a great sound with a floating bridge, but I've never seen one smaller than tenor size. I suspect that with a small soundboard and nylon strings, you need a type 2 bridge to get reasonable tone and volume.

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Andy Birko
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Re: Physics of bridges, tops and soundholes

Post by Andy Birko »

Chris Reed wrote: 2. Uke type, where the bridge/saddle combo act as a level at the end of the string, largely vibrating back and forth rather than up and down.
Everything I've read or heard from reliable sources contradicts your assertion of how the bridge vibrates. Although there is a larger component of back and forth on a pinned or tied bridge, it's still primarily up and down. This is borne out by the spectrograms of an instrument playing a note. Tension changes at double the frequency of the fundamental(up and down). If the primary mechanism for sound production was tension change (back and forth), the first partial would have an amplitude greater than that of the fundamental. i.e. it would sound an octave higher which it usually doesn't.
PMoMC

Owen Woods
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Re: Physics of bridges, tops and soundholes

Post by Owen Woods »

Rob Dick wrote:Thanks Owen. It's things like the effects of the rigidity or sound absorption properties of backs and sides, the concept of "driving" the top and how it's affected by various bracing and bridge designs, how and why soundholes work etc. that I want to get my head around.
Hmm, I know a bit about all of that (I'm in the middle of writing up my master's project report on string instrument acoustics), but I don't know enough practical information to inform anyone about anything. In fact, since my project is mostly experimental, most people on here will know more than me! In that, I can describe roughly how everything that you have just said works, but not say how you can exploit it. If someone does have a reference book that gives practical information on this sort of thing (bracing particularly) I would be really interested.

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Re: Physics of bridges, tops and soundholes

Post by Owen Woods »

p.s. just found a (probably illegal) e-copy of most of the guitar section of Fletcher and Rossing on t'internet. This is very much a scientific book, but depending on your background you should be able to get some understanding out of it, if not practical guidelines.

http://hajos-kontrapunkte.blogspot.co.u ... sical.html
(Link removed by Staff, please see our Policy)

Unfortunately the book itself is massively expensive. Might ask for it for a graduation present (only 7 weeks to go!)

Rob Dick
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Re: Physics of bridges, tops and soundholes

Post by Rob Dick »

Thanks Owen. That books has way too much maths for me but I'll work my way through it!

Here's an example. Some years ago when a mate had a guitar shop one of his customers picked up a really horrible banjo-mandolin at a market for a few dollars. Rather than rehabilitate the thing he removed the vellum and hardware and made a soundboard from a thin piece of King Billy Pine with just two short braces running lengthways and then glued on a uke bridge (imagine an H pattern if the top was transparent). He strung it with uke strings and brought it in to show us. His expectation was that it would sound like a cheap soprano uke but it was one of the most mellow woody things I've ever heard! For a uke it even had a little bit of sustain!

The thread on Tahitian ukes reminded me of that instrument, which then led me to thinking about the position and function of soundholes, bridge construction etc.
Rob

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Greg Robinson
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Re: Physics of bridges, tops and soundholes

Post by Greg Robinson »

Owen Woods wrote:p.s. just found a (probably illegal) e-copy...
Hi Owen,
Please, if you think it may be an "illegal copy", do not post links here. If the host (the website) is not the creator of the work (the copyright owner), or the host is not linked to by the creator, then that material is likely in violation of copyright law. The MIMForum has specific rules regarding copyrighted material to protect it from litigation.

Thanks for your cooperation.
MIMForum staff member - Melbourne, Australia

Chris Reed
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Re: Physics of bridges, tops and soundholes

Post by Chris Reed »

Andy Birko wrote:
Chris Reed wrote: 2. Uke type, where the bridge/saddle combo act as a level at the end of the string, largely vibrating back and forth rather than up and down.
Everything I've read or heard from reliable sources contradicts your assertion of how the bridge vibrates. Although there is a larger component of back and forth on a pinned or tied bridge, it's still primarily up and down. This is borne out by the spectrograms of an instrument playing a note. Tension changes at double the frequency of the fundamental(up and down). If the primary mechanism for sound production was tension change (back and forth), the first partial would have an amplitude greater than that of the fundamental. i.e. it would sound an octave higher which it usually doesn't.
I was writing too compressed. My understanding is that the string rocks the bridge back and forth, which translates to a rippling motion in the soundboard because the saddle, acting as a lever, is coupled rigidly to the soundboard. The consequence is lots of up and down motion in the soundboard, plus someother kinds of motion as well. The physics of how this translates into sound is beyond me.

My main point was that on a small soundboard this seems to produce more, and more complex, sound than a floating bridge.

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Re: Physics of bridges, tops and soundholes

Post by Owen Woods »

Greg Robinson wrote:
Owen Woods wrote:p.s. just found a (probably illegal) e-copy...
Hi Owen,
Please, if you think it may be an "illegal copy", do not post links here. If the host (the website) is not the creator of the work (the copyright owner), or the host is not linked to by the creator, then that material is likely in violation of copyright law. The MIMForum has specific rules regarding copyrighted material to protect it from litigation.

Thanks for your cooperation.
No problem. Not altogether sure whether it is illegal, as Google Books has extracts from it on there (but not all of it). Also it was from the first edition, which is no longer in print. It's mighty difficult to get hold of the second edition as well and it costs £60-£100, which is a lot. Noted about the forum rules, won't do it again :)

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Greg Robinson
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Re: Physics of bridges, tops and soundholes

Post by Greg Robinson »

No worries Owen, feel free to post a link to the Google books extracts, they normally include links to purchase the entire text if anyone is inclined to do so. Thanks.
MIMForum staff member - Melbourne, Australia

Michael Lewis
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Re: Physics of bridges, tops and soundholes

Post by Michael Lewis »

for those who want to understand these intimate workings of the structures of string instruments I suggest you spend time reading comments by Alan Carruth, and ask him some specific questions. Also Tom Rossing collaborated with Dave Cohen on a scientific paper on the acoustics of mandolins, which should be at least linked to on Dave's web site. They used laser holography to create virtual standing waves to show the vibrational modes of the plates. These guys are scientists and their use of words is specific, so if you converse with them choose your words carefully to express exactly what you mean to say. For example, the word 'theory' means a well ordered and mathematically supported statement that has not yet been disproved, like the theory of relativity. What we commoners often refer to as a theory is more of a loose conjecture, NOT a theory.

Rob Dick
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Re: Physics of bridges, tops and soundholes

Post by Rob Dick »

Thanks for that Michael. I've just pulled up Allan's profile and I'm madly opening up his posts to harvest some wisdom! ;-)
Rob

John Hamlett
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Re: Physics of bridges, tops and soundholes

Post by John Hamlett »

There are lots (thousands?) of scientific papers about violins, hundreds about guitars, and Drs. Cohen and Rossing are adding to the literature on mandolins. Most of it is available at libraries (including, I'm pretty sure, the Fletcher and Rossing book). Alas, much of it is pretty hard to read and understand for those of us who don't have a good handle on the language of science and mathematics (it is the math that goes quickly over my head), but I have many printed articles in my file cabinet and though I don't really feel that I understand it all, I'm able to get the basics from them. It doesn't hurt that Dave Cohen is a personal friend of mine and we've had discussions over lunch and such, where he can explain in simpler terms what is meant by the things that he and others have studied and written about.
You're on the right track; you've asked a question. Keep asking and keep reading. There is a lot to learn.

Rob Dick
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Re: Physics of bridges, tops and soundholes

Post by Rob Dick »

Hi John. I'm working from the Tahitian uke model as a starting point. I've never had the patience or skill to build traditional acoustic instruments (ukes, guitars and mandos) and there's never been a need as the Chinese and their CNC machines do it so well, but the Tahitian ukes got me interested in assembling a cross-over instrument that is as crude and simple to build as a solidbody (which I do have some experience with) and marrying that with the bracing issues of working with timbers of minimal thickness! I've just sourced some spruce and cedar top woods from Stewmac and my next step is to bring together what I've picked up from reading those websites (especially the Torres bracing as that seems most relevant to ukes). By using a bolt on Fender style of tenor uke neck all it will cost me as I experiment with bracing and soundholes is my time and a bit of wood, and I'm sure as I put the theories into practice I'll hear what works and what fails!
Rob

John Hamlett
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Re: Physics of bridges, tops and soundholes

Post by John Hamlett »

I neglected to point out that much of the physics involved in wooden topped instruments is very similar. Number of measurable modes and mode shapes may change from instrument to instrument depending on size and type of top and back, but the basics of how tops and backs (and the air within) behave is very similar whether we're talking guitars, mandolins, or ukes. even violins, with their bass bar and sound post, are more similar than different. Reading about guitars, violins, whatever, can reveal things that can guide us in whatever stringed instrument we're making.

Rob Dick
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Re: Physics of bridges, tops and soundholes

Post by Rob Dick »

I'm starting with a 7" diameter by 1 1/4" deep space, spruce top which I plan to take down to about 2.5mm, so not dissimilar to a ukulele/mandolin except a 40mm soundhole and using a uke bridge and some very basic bracing rather than a floating bridge. I figure if I can get soprano uke volume from a tenor scale instrument and after a month or so the top is still fairly flat then I've had a small win and more importantly I've got a starting point for ongoing experiments.
Rob

Owen Woods
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Re: Physics of bridges, tops and soundholes

Post by Owen Woods »

To that I would add the piano! Benade's book, which I have been dipping in and out of whilst writing this report deals with the piano in ways that can be transferred to guitar-like instruments, strange though it might seem. Yes, the strings are excited differently, but they are still vibrating strings on a wooden soundboard.

Chris Reed
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Re: Physics of bridges, tops and soundholes

Post by Chris Reed »

Rob Dick wrote:I'm starting with a 7" diameter by 1 1/4" deep space, spruce top which I plan to take down to about 2.5mm, so not dissimilar to a ukulele/mandolin except a 40mm soundhole and using a uke bridge and some very basic bracing rather than a floating bridge. I figure if I can get soprano uke volume from a tenor scale instrument and after a month or so the top is still fairly flat then I've had a small win and more importantly I've got a starting point for ongoing experiments.
2.5mm is pretty thick for that size, which is very similar to a soprano uke lower bout. I recently made a narrow-bodied soprano (5.75 inch lower bout) with a spruce top at about 1.9mm - 2.0 might have been better for tone, but it still sounded fine with the standard soprano minimal bracing. I wouldn't go any thicker than 2.2 mm, and probably less.

I think your biggest problem will be the depth - your top area is much the same as my uke, which was 2.5 inches at the tail and 2 inches at the heel. You might get similar volume, but it will be horribly trebly if the box is that shallow. Mine was only just not shrill.

If your box depth is fixed, you might want to consider starting with a smaller soundhole (35mm?). This will give you more bass, and you can always enlarge the soundhole later by wrapping some sandpaper round a funnel.

Your other challenge is to get the bridge in a good place - near the centre is ideal, or perhaps 2cm back from the centre like a banjo-uke. But your soundhole is then a problem because it takes up much of the top half of the soundboard.

On a soundboard that size I don't think you need any more than a single brace, about 12mm below the soundhole and about 6mm x 12 mm (W x H). Plus a bridge plate (sound board cutoff) which is 10mm wider than the bridge footprint all round. This assumes the sides are stiff, so the bracing isn't playing a major part in stopping the instrument folding in half.

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