Helmholtz / Slot Resonator Theory Question

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

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

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

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

John Sayers wrote:

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.

John Sayers wrote:

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.

John Sayers wrote:

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

:D: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

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

John Sayers wrote:

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

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

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.

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

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.

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

: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.

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?

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/cscie129/nu_lectures/lecture3%20/ho_helmholtz/ho_helmholtz.html ) Or is it something really specific to slat resonator?

Or is it something really specific to slat resonator?

Exactly, as well as other similar devices, such as perforated panels. If you work through the math, Barefoot actually explains it quite well. Volume is width times height times depth, but the width and height are not relevant (they cancel out), so only the cavity depth is what determines the frequency. - Stuart -

Alright I think I got it, the holes ratio is proportional to the box surface, so for a multi perforated plate or a slat plate the volume is no longer part of the formula for each emplacement on the plate; wich is not true of course with a single-hole panel, right? So a broadband angled panel should work with holes as well as with slats...

But the formula is considering a right angled box, so depth is directly related to the volume?? So it is not the angle that make it broadband but rater the difference of slat and slot's width... ?

so for a multi perforated plate or a slat plate the volume is no longer part of the formula for each emplacement on the plate; wich is not true of course with a single-hole panel, right?

Right.

So a broadband angled panel should work with holes as well as with slats...

Same principle, yes.

But the formula is considering a right angled box, so depth is directly related to the volume??

There is a relationship, yes, but since the volume scales exactly in proportion to the rest of the dimensions in this case, it is not necessary to consider it when calculating the frequency. For this case, the frequency depends ONLY on the depth, just like John pointed out originally,

So it is not the angle that make it broadband but rater the difference of slat and slot's width... ?

It is both, since angling the slats also changes the depth. With angled slats, the left end, for example, has more depth behind it than the right end, so the frequency will be different. As you move along the slat, the resonant frequency is, theoretically, different at every point, varying from the lowest at one end to the highest at the other. So, as Barefoot said, each slot is broadband, and therefore the "Q" for that slot is broader and flatter than it would have been if the depth were constant. In reality, it is a bit more complex than that, since the air "plug" in the slot doesn't really act as millions of tiny slugs, but rather it reacts "somewhat" like millions of tiny slugs and also "somewhat" as a single unit, which is why the entire wall tends to act as a single unit as well, that is both broadband and very effective. But the basic idea is to consider that the tuned frequency varies along each slot, according to depth ONLY, and that each slot has it's own tuned frequency range (defined by depth and neck dimensions), and when you combine all of those you get a rough idea of how the entire wall will behave. - Stuart -

Is it possible to go below 100Hz with those kind of absorbers? I have a big lack of bass between 60Hz and 110Hz in my mix-room, I ve tried to make a broadband panel around 85Hz, but the result is not really satisfying : Purple=without panel; blue=with panel I found difficult to make slats around that frequency (hudge slats and tiny tiny slots...) so I made holes, panel = 1m/1m50; 30cm right depth; 10cm left depth; thickness 34mm; holes spaced by 4,6cm; I made several lines of holes from 3mm to 10mm; bigest holes at the center of the panel; I closed the back-panel with a 5mm plywood because it will be against the wall I think the plywood shouldnt vibrate, everything hermeticaly closed, 5cm rockwool spaced a bit from the holes... I don't really know witch way to go... (here's the thread where Stuart's helping me http://johnlsayers.com/phpBB2/viewtopic.php?f=1&t=18002)

you won't fix the 85hz problem with a resonator. They aren't efficient at those low frequencies. It is a mode of your 3.91m dimension. So make some side panels - 2.4 x 1.2 mdf or ply sheet with insulation/cloth cover and angle them on your side walls on the 3.91 dimension. A room that small needs heaps of treatment - the treatment you have is only touching the fringe of your real need. cheers john

In fact I ve put a lot of absorption on the front wall, I thought curved Helmholtz was a good way to reflect 1st reflections without adding absorption on the side walls while helping a little bit on the low frequency absorption... I think I need wood because you feel good in a room when there is some wood right? So maybe I could put angled absorbing panel you're talking about on the back-wall? Thank you all of you guys for your precious help on this wonderful forum! http://johnlsayers.com/phpBB2/viewtopic.php?f=1&t=18002

So make some side panels - 2.4 x 1.2 mdf or ply sheet with insulation/cloth cover and angle them on your side walls

Sorry for my bad english John, I m not sure to understand everything... 2.4x1.2 is panel's height and lengh? should the insulation and plywood be thick?

Is it possible to go below 100Hz with those kind of absorbers?

Like John said: That type of device is not efficient at such low frequencies. Helmholtz resonators are far more useful in the mid-range. As you can see from your graph, it appears to be working (there is a small reduction in the mode at 88 Hz, but the effect is nowhere near as big as you need. That's why bass trapping is almost always done with either panel traps or with deep absorption. John is saying the same thing I said on one of your other threads: That room needs a LOT more treatment. It is a small room, and therefore will need a huge amount of low frequency treatment.

In fact I ve put a lot of absorption on the front wall,

Walls are not much use for bass trapping with absorption: Corner are. Walls are good for panel traps (membrane traps, which are pressure-based devices). Corners are good for absorption (which is velocity based). What you need are large bass traps in the room corners.

I thought curved Helmholtz was a good way to reflect 1st reflections

:shock: :?: :!: :shock: Why would you want to put REFLECTION at your first reflection points? That's where you need ABSORPTION! You should be reducing all first order reflections as much as possible, not making tings more reflective. You COULD do that if you angle it steeply enough to ensure that all first order reflections are going way past the listening position, but the small angle you are using for that perforated panel does not look like it is enough for that. Did you ray-trace to figure out the angles?

without adding absorption on the side walls

Why do you not want to put absorption on the side walls? That room is small, and needs lots of absorption anyway. 317 sabins of absorption, to be exact. In other words, roughly 50% of the ENTIRE surface area of the room needs to be perfect absorption: That means half of the floor, half of the ceiling, and half of each wall needs to be perfect absorption: Since it is not practical to put absorption in the floor, that means that your entire ceiling should b absorptive, plus 50% of the area of each wall. That is how much absorption you NEED, according to the equations. It is a small room, so it needs a LOT of absorption, and most of that needs to be aimed at low frequencies. So forget Helmholtz devices: they are not efficient and too hard to tune at low frequencies. They would take up way too much surface area, considering that half of each wall needs to be absorptive.

I think I need wood because you feel good in a room when there is some wood right?

You don't need wood to "make you feel good". You need wood where it is necessary to give the acoustic behavior that you need. That's why I suggested slot walls.

I found difficult to make slats around that frequency (hudge slats and tiny tiny slots...)

That's not the purpose of slot walls: They are not meant for low frequencies. Rather, they are meant as general broad-band devices, that absorb, reflect and diffuse all at once. They also work as absorbers at low frequencies (well below the tuned range), to a certain extent.

I closed the back-panel with a 5mm plywood because it will be against the wall I think the plywood shouldnt vibrate

5mm is way too thin, and it will vibrate. On a Helmholtz device, the cavity needs to be rigid. That should be 19mm plywood at the back and on the sides. - Stuart -

Sorry for my bad english John, I m not sure to understand everything... 2.4x1.2 is panel's height and lengh? should the insulation and plywood be thick?

yes - you are trying to divert a wave that you could surf on if it were a water wave. As Stuart said, thin plywood is insufficent. as i said before - small rooms need lottsa treatment. and the REAR wall is you major wall and you need to angle your side walls. It's all laid out in the recording manual if only you'd take the time to read it! check my signature, draw up a chair and read it. cheers john