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Trying to understand the limitations of Helmholtz resonators in LF absorption

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Delrin

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This not only seems odd with the tube resonators I use but also with practically every ‘bass-trap’ designed for and placed in a corner.

Don’t you think?

The comments I've heard elsewhere, stating that an absorber should span the entire wall of a room, were in relation specifically to Helmholtz absorbers. No physical basis for this statement was given, and maybe it is incorrect (that is the kind of thing I'm trying to figure out in this thread). The intuitive appeal is that a pressure-based absorber encompassing the entire wall will conform to the entire zone of maximum pressure at the room boundary (assuming for simplicity that we're talking about a fundamental axial mode and allowing for the dimensions of the absorber).

I would think the typical corner bass trap is usually understood to be a velocity-based absorber, which (unlike a Helmholtz absorber) has no frequency selectivity to speak of. It would seem that the advantages of placing these in a corner are that (1) they will act on two or more room modes (eg left/right and front/back), for which the potentially different frequencies are less of a concern for the broadband absorber, and (2) the use of corner-straddling traps allows the absorbent material to be placed further from the wall, which is advantageous for a velocity-based absorber. I have also seen it stated, in a number of forums, that treating the entire wall surface with porous absorber is even better than treating just the corners but that the space incursion becomes more of an issue for a given absorber depth ("better" for modal control but not getting into the possible desire for diffusion and preservation of some higher frequencies to avoid excessive "deadness").

In regards to large tube resonators: I have had trouble visualizing how the relatively small mouth area of a single such device can affect the modal sound pressure that extends over an entire wall. Naively it seems like this would require some non-intuitive "action at a distance". I will elaborate on this in a separate post.
 
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Delrin

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This not only seems odd with the tube resonators I use but also with practically every ‘bass-trap’ designed for and placed in a corner.

Don’t you think?

Here's a simplified thought experiment that might reveal flaws in the way I am thinking about large tube resonators:

Imagine an "ideal" room that has some rectangular geometry. The length, width, and height are sufficiently different that we can consider the fundamental axial modes as having distinct frequencies. There is no furniture, and no treatment is applied in the initial condition (assume walls/ceiling in multi-layer drywall with a concrete floor). A continuous pure tone corresponding to the first axial mode of the "length" dimension is played on a speaker. The sound field in the room will consist of the radiated and reflected wavefronts from the speaker, plus the axial length mode excited by the pure tone. Let's suppose this axial mode has a frequency of 50Hz, corresponding to a wavelength of 6.8 metres (meaning the room length is half that, or 3.4m). Let's also assume that the area of the back wall is 30 square metres, and that the room is situated within a much larger space in which exterior walls are far away from our inner room.

The first axial modes for width and height are sufficiently different that only the length mode is excited by the pure tone that is played. Consequently, this mode is associated with a uniform zone of maximum pressure over the entire back wall (there is also the direct and non-modal reflected sound from the speaker).

In an effort to attenuate the length mode, we cut a single circular hole with a diameter of 25cm in the back wall (the exact location doesn't matter because the zone of maximum pressure is uniform over the entire back wall). We have now removed 0.05 square metres of the reflective boundary that was supporting the length mode. Because the sound wavelength of 6.8m is much larger than the hole diameter of 0.25m, the hole will emit hemispherical wavefronts into the large outer space surrounding the room.

Because all sound energy impinging on (and diffracting out of) the hole will be forever lost to the room, one might assume that this is the absolute maximum "absorption" that can be achieved over the 0.05m2 circular area. This leads to the following questions:

1. Can we reasonably expect such a small hole in the back wall to provide significant attenuation of such an otherwise expansive standing wave?
2. Can the mouth of a single Helmholtz resonator perform better than an aperture of the same size opening out into a large empty space?

I'm making a few assumptions here that could well be wrong. For example, the hole in the wall opening to free space could conceivably have impedance properties at 50Hz that cause partial reflection of the impinging wavefront back into the room. This also highlights the differences between modelling absorption of "ray-like" high frequencies and "wave-like" low frequencies...

I think that working through the concepts and possible errors in the above simplified model might help understand the situation.
 
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Geert

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There are warnings about the perils of on-line Helmholtz calculators, many of which are purported to give incorrect results.

Lots of online calculators are based on a wrong formula, and don't/didn't include the mouth correction factor. Full story by the well respected acoustic designer Eric Desart (RIP):
There was some confusion about the origin of this error. Both Master Handbook of Acoustics - F. Alton Everest and Handbook for Sound Engineers - Glen M. Ballou were referred as possible source. I took liberty to check different editions of the books themselves. The formula with the included error is:

1260*sqrt(r/((d*D) + (r+w)))

This error does NOT originate from "Master Handbook of Acoustics" but from "Handbook for Sound Engineers"

2160*sqrt(r/((d*D) * (r+w))) [+ sign to be substituted by *]

Both Handbook for Sound Engineers: editions 2 and 3 still show the faulty version.

d = the effective depth of the slot in inches, which is approximately (1.2) x (thickness of the slot in inches)

Important to note is that the factor 1.2 is an APPROXIMATION. The correct mathematical modelling of the mouth correction for Slat type Helmholtz resonators is a rather complex business.

What is this mouth CORRECTION? A Helmholtz resonator is a mass-spring system, which is comparable with a panel or membrane RESONATOR. The system is based on a mass which vibrates in resonance on a SPRING. The ratio of the mass versus the dynamic stiffness of this spring defines the resonance FREQUENCY. The air layer in the cavity acts as a spring with a certain dynamic stiffness mainly defined by its volume.BThe larger the Volume, the weaker the spring becomes (lowering resonance frequency) and vice versa.

For a panel resonator it's easy to imagine what the mass is: the PANEL. The heavier this mass becomes the lower the resonance frequency and vice VERSA. As such a panel resonator is mainly defined by the combination of both PROPERTIES. This isn't complete, since angle of incidence, weakness of spring, damping etc. will influence the resonance frequency and the Q-factor.

For a Helmholtz resonator this mass is represented by the mass of the air enclosed by the neck or slot of the resonator. However this apparent mass extends outside the exact geometrical boundaries of this neck or SLOT. This is covered by the mouth correction, which is in fact a correction factor increasing those geometrical BOUNDARIES. In reality this phenomenon is much more complicated than the simple factor, used by the traditional FORMULAS. As such the distance between those necks or slots (interaction) and others will influence this CORRECTION. For practical use however the standard formulas are a good approach.
 
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sarumbear

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Maybe we need to distinguish between what's 'ideal' (as mentioned by Andy Mac Door) and what's often good enough.
If you can define them, we can attempt to distinguish.

My definition for an ‘effective’ resonator is simple: it’s a device that absorbs the room resonances so that the RT60 is uniform across the 20-400Hz range, where the wavelength is larger than the objects in the room.
 

sarumbear

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1. Can we reasonably expect such a small hole in the back wall to provide significant attenuation of such an otherwise expansive standing wave?
2. Can the mouth of a single Helmholtz resonator perform better than an aperture of the same size opening out into a large empty space?
Replace resonator with driver and you may understand your confusion.

Just because there’s a resonance, it doesn’t mean it is enough to absorb the resonant energy in the room. The same applies to subwoofers. You can generate 20Hz from a 4" driver but at what level?
 
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Delrin

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Replace resonator with driver and you may understand your confusion.

Just because there’s a resonance, it doesn’t mean it is enough to absorb the resonant energy in the room. The same applies to subwoofers. You can generate 20Hz from a 4" driver but at what level?

Agreed - I'm still trying to get my head around how a room mode bouncing between 30 square metres of wall, excited by a 350W ported sub with 11" driver, can be "cancelled" by a single Helmholtz resonator neck at the end of a 25cm diameter tube (even if the tube is very long, equipped with suitable porous absorber, and tuned to the correct frequency). But isn't that what you are using in your home theatre? I understand you are using multiple tube resonators - I thought these were respectively for different modal frequencies though (and perhaps I have misunderstood the geometry used in your tube resonators).

As I mentioned earlier, I would be very interested in replicating one of your tube resonators for some "bench top" testing if you can provide additional implementation details (I understand they are large but this is not an issue). As you have studied acoustics you may well be working in this domain and are of course within your rights to consider this information "proprietary", so no problem if you'd rather not. My interest is purely academic and I have no commercial stake in any of this.

The example (noted earlier) in "Master Handbook of Acoustics" also implies that a single concrete forming tube, with a single short section of smaller pipe for the neck, can largely negate a 47Hz room mode. This seems counterintuitive in the same sense that using a 4" bass driver is counterintuitive.
 
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OldHvyMec

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1. Can we reasonably expect such a small hole in the back wall to provide significant attenuation of such an otherwise expansive standing wave?
2. Can the mouth of a single Helmholtz resonator perform better than an aperture of the same size opening out into a large empty space?

If I understand what you are saying you are correct. The hole size in a fixed helmholtz design is the only thing that matters for the actual
frequency you are canceling. It is NOT a trap. It is neutralizing the wave. The question is "If the wave your dealing controlled to the point
you want or do you want to eliminate the PEAK all the way to a complete VALLEY?"

A helmholtz adjustable is and can be used the same way as a DBA sub/bass system. Literally the more the merrier.
There is a point of diminishing returns on both. It always depends on the ROOM size and how you pressure it.
Is the room PORTED or and open design? They are called resonators NOT TRAPS. There is a reason.
I think of them as a tuned pressure regulator for a specific pressure I want to maintain or change if the room size or the frequency
load is increased. The starting and ending point of a resonator can have 2, or 3 different notches and depending on the number
can be very accurate. The trick is to not have the room looking like the inside of the old MIR space station.

I enjoyed a person call Master M over at the AG forums. I named him. Look at his room. Seriously LOOK at his 2-3 year experiment.
You will be amazed. He took Helmholtz, 500.00 dollars and really became a happy fellow. The room is something.

He never measured a single thing. The plates and wires and passive materials he used were from the trash.

Then Dennis evaporated. I miss that guy. Tesla/MacGyver/OCD guy. Worked for me. SS Sansui buff too.

Regards.
 

theREALdotnet

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Holmz

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Yes, that is very clear. That is the method which I also used to determine the exact absorption frequency of the HR box. The impact on room acoustic is modest.


That is exactly the way how the 11th-19th century churches in my country (and over wider area) were acoustically treated - many clay pots-jugs built inside the church walls, with only openings protruding outside. Pots/jugs are partially filled with ash as a damping material.

Nothing beats the ashes of those burned at the stake to add soul to the presentation.
 

OldHvyMec

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They didn't burn people only witches. They had to pass the dunk test too. If they sink they are fine if the float. That's not so good.
Party Pooper. I thought we were talking about tuning the temple. I'm glad we're not talking about Vlad the Impaler. He definitely
left an impression.

About the resonator holes, they catch, they don't pitch. I suppose there is an attraction, I never thought about it. :)

Regards
 

Bjorn

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I believe the main reasons why we see so many fail attempts with Helmholtz' (and other bass traps for that matter) is because of:
1. Not optimal placement
2. Too small units
2. Not covering enough surface area.

Below are some before and after meausurements in small rooms with the use of Helmholtz resonators.
Before.gifAfter.gif

Untreated.gifHalfway treated.gif

1.gif2. Etter.gif

bassrespons før helmholtz.jpgbassrespons etter helmholtz.jpg
 

Geert

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If you can define them, we can attempt to distinguish.
* Ideal: full coverage of walls or whatever solution "that absorbs the room resonances so that the RT60 is uniform across the 20-400Hz range"
* Good enough or effective: what, for a certain user, gives a result worth the effort taking into account practical limitations. (Remaining imperfections can maybe still be improved with DRC).

Which of both applies to the tube resonator solution you implemented in your living room? I think that's what the OP wants to understand.
 

Geert

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Can we reasonably expect such a small hole in the back wall to provide significant attenuation of such an otherwise expansive standing wave?
One or two 'PSI Audio AVAA' active bass traps the size of a subwoofer are usually insufficient to fix room modes...
 

OldHvyMec

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I believe the main reasons why we see so many fail attempts with Helmholtz'
They started but didn't finish, you are correct. It always works. Own up to the lack of a finished product, I say!
Was helmholtz applied and was there enough application to address the issues.
Fixed resonator (not traps) have their limits as to what they effect. You can adjust the hole size and even
have different size holes for different frequencies on the same baffle face. Users are limiting the ability of the tech.

You can tune a pyramid and they did several thousand years ago. Do some research it's very interesting.

BTW no DSP required, just mechanical tuning. I've yet to listen to any DSP tuned system I could set down and really enjoy.
I think it's a mental thing. I'm not kidding all my animal leave the room with sound effect from a DSP HT system. The same
concert with room treatment, helmholtz resonators and my bass system is The STEREO is to die for. Simple, known treatment
that work when applied correctly. I don't fill the tank and forget to check the oil, flat tires and the wiper blade scratching the
1000.00 windshield. In a hurry right. :cool:

The things I've seen in the name of being right and lazy. Mercy..

I've often wondered if destructive harmonics, like that of a hydro electric dams produce, would benefit if only to keep workers
safer through the use of helmholtz. Exposure can be horrific to the over exposed worker. You will spit your teeth out if you don't
use and isolation suit, limit the exposure time and the frequency of exposures. It is cumulative and it's deadly.

I'm not sure about the neighbors bone health, they punch it Baby, I'm sure they have crumbled a bone or two.
Thank god for spandex I guess. The blob.. Turn it up honey, my bones are healing again. LOL

Regards.
 

Vladimir Filevski

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I believe the main reasons why we see so many fail attempts with Helmholtz' (and other bass traps for that matter) is because of:
1. Not optimal placement
2. Too small units
2. Not covering enough surface area.

Below are some before and after meausurements in small rooms with the use of Helmholtz resonators.
View attachment 260253View attachment 260254

View attachment 260256View attachment 260258

View attachment 260261View attachment 260262

View attachment 260264View attachment 260265
Excellent results, bravo!
Please share some details about the size and number of Helmholtz resonators in that room?
 

Bjorn

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Excellent results, bravo!
Please share some details about the size and number of Helmholtz resonators in that room?
These are not mine but measurements from other projects. But in order ot treat very low frequencies with large wave lengths effectively, treatment also needs to cover a large surface area. So when people are buying something like a few units of a product you see below to work at 50 Hz, there's no surprise it wont't do much.
15539315_800.jpg

I have considered releasing Helmholtz resonators to the market for years and have design ready that I'm comfortable will work. But I'm not sure there's a market when the product is quite large and with a depth of either 20 cm or 30 cm. Especially considering that the Modex plate (VPR) is only 10-11 cm in depth and also has the benefit of being combined with absorption or diffusion in front making it more broadband and usable at places with specular energy. Something that's not possible with a Helmholtz. Unfortunately though, the VPR bass trap with steel is expensive.
 

thewas

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Both are without smoothing. The first one shows the room completely untreated, hence all the comb filtering.
Ok, as just typical Helmholtz resonators wouldn't smoothen up the higher frequency part as much.
 
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