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Helmholtz resonance math
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Roverharp
73 posts
Jan 30, 2020
1:35 AM
I’m trying a couple experiments with comb chamber size and would like to get some objective math to help my understanding.

The resonant frequency of a chamber is determined by the equation:

f=c/2pi x sqrtS/Vl

Hope that’s legible. Doesn’t seem to like math symbols. Anyway, S is the area of the harp hole and l is the chamber length but what consitutes V?
Or is it the reed slot one of the variables?

Bueller? Anyone, anyone?

Last Edited by Roverharp on Jan 30, 2020 1:42 AM
IaNerd
77 posts
Jan 30, 2020
12:05 PM
http://hyperphysics.phy-astr.gsu.edu/hbase/Waves/cavity.html
IaNerd
78 posts
Jan 30, 2020
12:07 PM
V is volume
Roverharp
74 posts
Jan 30, 2020
4:27 PM
I should have been more clear. Yes, V is for volume but volume of what?

Blowing across the top of a bottle is the most common example of a Helmholtz resonator. The bottle has a skinny neck that opens up to the larger body.

On harp I assume the chamber is the neck but what serves as the body?
dougharps
2059 posts
Jan 30, 2020
8:53 PM
Wouldn't your oral cavity and airway be the resonance chamber? That is why we learn to adjust to different pitches: to create the resonance that makes good tone. The small reed chamber is more like the bottleneck.

Doug S.
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Doug S.
STME58
2085 posts
Feb 01, 2020
10:43 PM
The university of New South Wales department of Music and Physics is a good resource for topics like this.

http://newt.phys.unsw.edu.au/jw/Helmholtz.html
Ger Scheeve
1 post
Apr 17, 2020
1:29 PM
Hi
Before you spend lots of time on theoretics,
Is it an idea to experiment with different chamber sizes, by varying comb thickness for instance. Or maybe extra long chambers that can be filled by turning in a screw, that's a thing I have been fantasizing about for decades now.
Birds don't know Bernoulli's law, but they fly so much better than a plane!

Last Edited by Ger Scheeve on Apr 17, 2020 1:30 PM
mx
38 posts
Apr 17, 2020
8:29 PM
how about this for how this works
PV=nR/t
so : n,t =constants we don't need
P = pressure (how hard i suck )
V = volume (how much air i move)
R = rate (how fast i move the air)

PV=R or R/P=V or R/V=P
MX
nacoran
10253 posts
Apr 18, 2020
3:35 PM
Ger Scheeve... on that line of thought, maybe offset the reed plates? If you had a really large chamber I'd think the blow and draw reeds would respond differently. For a blow note if the reed plate were still at the front of the harp the air would have to go all the way to the back of the chamber before enough pressure built up, I'd think, so having them recessed farther back or far forward would result in slightly different results.

I like the screw idea.

I've thought, for a long time, that you might be able to make reeds more responsive by shrinking the size of the chamber (less air needed to change the pressure). One thought I had was you could bevel the end of the reed chamber so that blow reed, on the down swing, is used sort of like you'd use a string to draw a circle. Basically the end of the chamber would follow the line of the tip of the reed. Since the draw reed swings the other way the bevel wouldn't get in it's way.

Of course as the blow reed swings up above the reed plate you wouldn't have the same tightness. I have this little plastic toy that uses a weight on the end of the reed and a little strip on the end of the reed at a right angle to the reed, to create this uneven airflow. The whole thing is a whistle combined with a free reed combined with a slide whistle that creates this bird chirping sound. It's actually pretty clever. Actually, now that I think about it, it's quite possible you could use a design like this do do some pretty neat tests. The slide whistle part lets you control the size of the chamber with really good accuracy.

https://youtu.be/qaUGK-SuiHw

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First Post- May 8, 2009
Ger Scheeve
3 posts
Apr 20, 2020
12:03 PM
Nacoran ...
Yes, that's what I mean. some kind of slide in an extra long chamber. Or a screw that fills up the chamber when you turn it inwards. You could even turn it inwards between the reeds, making the volume smaller than normal. And then play, adjust,play, adjust, etc. Who knows what it will do to the draw and blow bendability, and the overblowability!


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