Helmholtz / Slot Resonator Theory Question

[bolehnggak]

Hi,

I'm not yet experimenting with the slot resonator, but I would to get in depth with it purpose and how it works.
What I've read is that the example of a Helmholtz resonator, is when you blow a bottle from side, then the bottle would produce a note, right? And then when you put some absorbing material inside, the note would be reduced, because it changes the sound energy to heat, right?
But I wonder, doesn't it alsop change the volume of the bottle, so I suppose the fundamental note of the bottle would be affected?
Any thoughts or wisdom are really welcome.
Thanks.

Ari

[John Sayers]

The note is determined by the depth of the bottle, the insulation wouldn't change the volume very much as it's mainly air.

cheers
john

[bolehnggak]

I see. But then, how is the theory apply to the slot resonator? Because from the example of slot resonator, the insulation used is thick rigid fibreglass. That is certainly not just an air, I mean the fibreglass would definitely reduce the volume of the room inside the slot resonator. Or not?
And more questions.
How can I determine which frequencies will become the culprit of the room, so I can treat them with slot resonators? Because if I use the room calculator to measure all those nodes, the room is assumed to be empty. But if I put slot resonator, other acoustic treatment, then gear, then all table, chair, etc, it would change the result of the calculated one I assume. So what's the use of the calculator anyway?

Ari

[John Sayers]

Ari - I'll answer both your posts here.

I never design to remove a single frequency - I build resonators to be as broad band as I can - so does Ethan with his traps I think.

All this endless talk about room modes goes out the window the moment you add angular treatment because the geometry changes. Have you ever seen a pro control room that was rectangular??

Where I differ from the "Acousticians" is that I design a control room for listening to a pair of speakers, from the engineers point of view. It's all based around the symmetry of left and right, where the reflections go, what the listener will hear etc. because I come from a background of producing and engineering, not acoustics.

If you want to argue about the foam in the bottle - go and ask at yahoo's acoustic site

cheers
JOhn

[bolehnggak]

All this endless talk about room modes goes out the window the moment you add angular treatment because the geometry changes. Have you ever seen a pro control room that was rectangular??

That's my point. Actually my other posting about cloth covered bass trap also asking the similar question. I'm still learning so I'm hoping that you experts would be patient with me for so many questions and curiosity. Thanks John.

Where I differ from the "Acousticians" is that I design a control room for listening to a pair of speakers, from the engineers point of view. It's all based around the symmetry of left and right, where the reflections go, what the listener will hear etc. because I come from a background of producing and engineering, not acoustics.

But your experience in designing proper acoustic recording studios makes you an acoustician. Perhaps, a "recording studio acoustician"?
I actually more interested in learning from you guys, because you are talking from both side of the corner. You look not only from acoustician's side of view, which is full of theory and calculation but also from engineer's side of view, which its only goal is to hear the best sound out of the room.

If you want to argue about the foam in the bottle - go and ask at yahoo's acoustic site

Don't know about that. Maybe enough question. I only want to make my room sound good.

Ari

[John Sayers]

:D Ari - if you look at the formula for a resonator there is no mention of volume - only depth. It's the depth from the wall and the slot dimensions that determines the frequency - not the volume.

cheers
john

[barefoot]

Just to clarify the techi part:

Up to a point, the insulation in the cavity will actually tend to make the effective volume larger. It has to do with thermodynamics and the fact that the insulation reduces the heat transfer between the air molecules. An effectively larger cavity means a lower resonance frequency. However, adding damping to any resonant system raises the resonant frequency. So, these two factors tend to cancel one another out.

How close the insulation is to the slot tends to be a more significant factor than the actual amount of insulation. For some fixed amount of insulation (i.e. fixed effective volume) bringing the insulation closer to the slot will increase the damping and in turn raise the resonance frequency, as well as flatten and broaden out the peak.

Thomas

[barefoot]

if you look at the formula for a resonator there is no mention of volume - only depth. It's the depth from the wall and the slot dimensions that determines the frequency - not the volume.

John,

In the case of a slot resonator depth and volume are essentially the same. Assuming everything else his held constant the resonant frequency of a Helmholtz resonator is proportional the square root of the neck area (A) divided by the volume (V).

f = K*sqrt (A / V)

In a slot resonator all the slots act in tandem as a single neck. The neck area is then given by the ratio (R) of the slot width to the sum of slot width plus the slat width all times the total width (W) of the resonator times the total height (H) of the resonator.

R = slot width / (slot width + slat width)

A = R*W*H

The entire volume (V) of the slot resonator then acts as the volume of the Helmholtz resonator. And the volume is given by the width times the height times the depth (D).

V = W*H*D

Substituting into our resonance frequency equation we get:

f = K * sqrt (A / V) = K * sqrt ((R*W*H) / (W*H*D))

W and H cancel out from the numerator and denominator giving:

f = K * sqrt (R / D)

So, the resonance frequency is just proportional to the slot width ratio divided by the cavity depth. The only reason this is true for the basic slot resonator design is because the neck area directly scales with the two other volume dimensions.

Make sense?

Thomas

[John Sayers]

Yeah - It makes sense - but all you've proven is that volume is involved in the creation of the formula - as you have shown the volume factor cancels itself out and is not relevent. So in answer to the original question - i.e. will the insulation make a difference by changing the volume - the answer is no.

cheers
John

[LDQ]

Speaking of slot resonators....

1. I just finish building a triangular shape slot resonator for my vocal booth. Is there anyway that I can test it to make sure it is working correctly and that I didn't mess up somewhere.

2. Is it OK to cover the slot resonator's front insulation with plastic then cloth then slats?

Let me know.

Cheers,

Luis.

Check out the pick.

[John Sayers]

you shouldn't need the plastic with the cloth cover Luis. I'd leave it out.

cheers
john

[LDQ]

Ok I will leave it out....but John or anyone else...how about my other question...how can I tell the slot resonator is working correctly. By ear? measuring the overall room response when it is finished? Any thoughts????

Luis.

[John Sayers]

you should notice the difference by ear Luis- check out the sound of your and otherrs voices in the room as you add the treatment. If you play loud music in the room you will feel the air moving in the slots if you put your hand over them.

cheers
john

[saint gillis]

Ari - if you look at the formula for a resonator there is no mention of volume - only depth. It's the depth from the wall and the slot dimensions that determines the frequency - not the volume.

So if you make an angled slat-wall or Helmholtz resonator (with holes), if you determine the frequency at the highest depht and at lowest depth, will you got your absorbtion range?

[saint gillis]

I don't really understand Barefoot's demonstration..
Volume is always involved in the classic Helmholtz formula (for instance http://people.seas.harvard.edu/~jones/c ... holtz.html )
Or is it something really specific to slat resonator?