Body resonance measurement using cardboard prototypes

For my 1st build project I’m considering a paddle shape ukulele with a neck available from Mainland in a concert size. I found several design references to body and top tuning that recommend targeting whole notes (no sharps / flats) to avoid “beating frequencies” with more common playable notes, and in the case of the body volume resonance, below the lowest note playable on the instrument. Also found is a reference for a standard concert size body resonance of about 225 Hz (“A” note below the C on the open 3rd string).

I verified this by testing a concert size uke that measured close to this frequency. My testing rig consists of me blowing across the sound hole while recording the sound using the freeware Audacity software with a good quality microphone. Audacity has a handy spectrum display feature that I can read the frequency of the largest peak and I assume this is the resonating body / sound hole combination.

I built two prototype paddle bodies out of double wall corrugated cardboard (image attached) and tested them. The smaller one is sized close to the Boat Paddle Ukulele Company concert uke, about 12” x 6.5” x 2.5” (H,W,D) in size. This looks to be smaller than my standard guitar shaped concert uke and I expected a higher pitch resonance tone. To my surprise the frequencies measured are much lower than expected. The concert prototype resonates at 140 Hz (C#-D3), the larger body 110Hz.

Does anyone have any suggestions or comments regarding this method of testing body size prior to actual wood fabrication or why the paddle shape is so much lower in tone than a more standard shape?

Thanks!

Do you think you're "measuring" the air resonance (aka Helmholz) or the main top resonance? To make it more difficult, they're coupled.

Paddle shaped would have a larger volume of air and a top that is less broken up into two distinct small areas.

Read Carruth, Cohen, Siminoff, and Hurd for starters... Then Hutchins, Rossing, etc...

cardboard prototype

I want to get the "Helmholtz" of the body volume / hole to help size the top before actual fabrication. Maybe I can repeat the test with a ruler attached across the top to stiffen it.

On a related subject, my calculations of the frequency using the Helmholtz equation is not even close to what I am getting. Is this normal?

Thanks for the comment.

Bruce

BruceCrook said:

I want to get the "Helmholtz" of the body volume / hole to help size the top before actual fabrication. Maybe I can repeat the test with a ruler attached across the top to stiffen it.

On a related subject, my calculations of the frequency using the Helmholtz equation is not even close to what I am getting. Is this normal?

Thanks for the comment.

Bruce

Click to expand...

I always thought the Helmholtz equation was more applicable to non-vibratory, rigid structures.
Have you looked at David Hurd's web site discussing resonances?
http://www.ukuleles.com/Technology/Meyer.html

True Helmholz air chamber coupled to outside air resonance has totally rigid walls. That's certainly one issue here.
I have to tell you, you're on a very slippery slope. Going at this "scientifically" before you even build an instrument will probably yield you nothing useful. Just build a uke. Then start studying...and go down the slippery slope. Every single instrument I've ever heard that was designed "science first" was mediocre at best. That is not a slam on a scientific approach, but it can easily lead you astray...very quickly. You'll tend to focus on one aspect, totally ignore others and you'll wonder why, for instance, your numbers do not match your results...which just happened to you. You need a more holistic approach. Like I said, look up the science monsters of lutherie I mentioned. They have blazed the trails...plural...unfortunately!

I agree with Rick.

For your first build you don't need to worry about air chamber resonance, tap tuning the plates, etc. One thing to keep in mind when measuring the Helmholz resonance is that you've placed the soundhole way at the end (neck end), in fact so close to the end you wouldn't be able to build the uke with it in that position. In any case, the length of the chamber also affects the resonance frequency - if you want to compare values, you need to place the soundhole in the same position as your reference uke, and it also needs to be the same size (absolute or relative to the box volume). If I understand your post correctly, the uke you have there is not the one with 225 Hz that you're comparing to, right? Why don't you just measure the volume and chamber resonance of your concert own uke for reference?

Rick Turner said:

Read Carruth, Cohen, Siminoff, and Hurd for starters... Then Hutchins, Rossing, etc...

Click to expand...

Good points, Rick, and a good reading list. May I add Trevor Gore's book?