Trying to understand the limitations of Helmholtz resonators in LF absorption

[Delrin]

Hi all,

Helmholtz resonators are enticing for the control of low frequency room modes, and it's remarkable that such small structures can resonate at such low frequencies. However, they seem to have been largely written off by the audio community because they so often fail to perform as expected (there are many online accounts where considerable effort is devoted to building an HR absorber that seems to do nothing at all acoustically).

I am attempting to visualize what's going on physically with Helmholtz resonators under different conditions. The hope is to better understand why they succeed or fail in various absorber applications. There is a body of published academic research on this topic, and I'm trying to reconcile this with "real world" observations that can be made without access to an impedance tube or a reverberation chamber. I am interested in the 40-50Hz range, which is typical of modal problems in small rooms, and for which an impedance tube would be difficult. I also realize that an optimized multi-sub approach, coupled with broadband porous absorption, is the recommended solution in such cases. The focus in this thread is specifically on how Helmholtz resonators work (in acoustic absorption, not speakers) and why they so often fail especially at low frequencies.

The approach I've settled on is to consider "classic" Helmholtz resonators, like beverage bottles, as well as constructions that are typical of DIY or commercial acoustic absorbers (eg perforated MDF with an airtight backing cavity). I am starting by looking at the behaviour without any absorbent material in the cavity, as the physics are more predictable and easy to interpret.

In general, I've noticed a few interesting things:

1. Bottles, regardless of their size, are easy to "excite" by blowing at a grazing angle across the neck. An audible pure tone is generated, at a frequency that scales roughly with the inverse square root of the bottle volume (in accordance with the expected physics and allowing for differences in neck dimensions). In contrast, I have been unable to excite an MDF box in this way (I have tried various means by blowing and directing streams of compressed air at a "grazing" angle). This might be due to the fact that the resonator "neck" is flush with the MDF surface, or it could reflect some (hypothetical) intrinsic damping of the MDF hole construction (see point 2).
2. The MDF boxes I have built all exhibit an "air jet" emanating from the hole, which occurs at the expected resonance frequency and which is able to strongly deflect a candle flame (see video link below). This is evidence of "vortex shedding", which can introduce non-linear resistive losses. None of the bottles I tested deflect the candle flame, suggesting that the flared mouth of the bottles reduces the vortex shedding effect (compared with the sharp hole edges through an MDF panel). This might explain why the bottles are easier to excite than the MDF boxes, and (possibly) why the bottles appear to be more acoustically "reactive" than the MDF constructions (see point 3).
3. All of the bottles I tested are capable of producing marked acoustic effects around the mouth during a tone sweep. This appears as a strong bipolar fluctuation in the frequency response, which is consistent with the imaginary component of the acoustic impedance crossing through zero at the resonant frequency (this is pretty much the textbook definition of resonance). In contrast, the MDF boxes I built do not cause any change in the acoustic frequency response curve around the resonance frequency (despite the fact that they all deflect candle flames at their resonant frequency). Note that these observations were made by placing a measurement mic near the mouth of each resonator during a tone sweep (the resonator mouth was facing the speaker). This is not the same as measuring the absorption coefficient, but the results should provide a qualitative picture of how the impedance is changing with frequency.

Conclusions so far: people aren't kidding when they say Helmholtz resonators are hard to build and tune. I suspect that the physics gets messy at very low frequencies (like below 50Hz) and that there may be non-linear effects that are worse in perforated MDF and are beyond the ability of popular calculators to model. This seems to be an active research topic in academic circles, and there is a lot of information to digest. I would not write the approach off for low frequencies, but would caution that it's not easy either.

Below are some photos of the MDF boxes and bottles I've used in my testing, as well as a demonstration of acoustic effects produced by the bottles. I think I will move away from MDF boxes (at least for experimentation) and use ABS pipes, as these are easier to control. If I get a better handle on the physics, I might go back to MDF boxes.

Here are some MDF boxes made from 3/4" MDF. The cavity size for the two small boxes is 4x4" with a depth of 7.25" for the smaller box and 12" for the longer of the two "single cell" boxes. The larger box is 6' tall x 22" wide and also has 1/4" holes in 3/4" MDF, with a cavity depth of 7.25" and a hole spacing of 4" centre-to-centre. The theoretical resonance frequency (undamped) for the 7.25" deep boxes is around 40Hz (based on Matlab code from Cox & D'Antonio's book "Acoustic Absorbers and Diffusers"). They do exhibit resonance at this frequency, but only via the "candle deflection" test. They have no acoustic effect at all, either on the room or right at the mouth of the resonator cells. For some tests, I machined a plastic insert for the hole and press fit this into a larger hole in the MDF. The idea, with the plastic inserts, was to better control the hole diameter and surface finish. This would also allow a chamfer to be applied to the hole edges to potentially reduce vortex shedding.



Bottles: I've been using four bottles with volumes ranging from 150ml to 3.8L. All of these can be made to emit a pure tone by blowing across the mouth, and they all produce a marked effect on the sound field around the resonator mouth during frequency sweeps (at frequencies corresponding to the pure tones they emit). None of the bottles can cause deflection of the candle flame though.



Here are frequency sweep curves in REW for different bottles. A measurement mic was placed near the mouth of each bottle during a frequency sweep. In each case, the bottle mouth was facing the speaker driver at a distance of around three feet. Only the single speaker was playing, and the sweep volume level was set according to the REW instructions. Speaker was a Focal Solo6 and does 40Hz no problem, mic was a uPrecisionMic from Studio Six Digital. Similar results were obtained using a subwoofer and other bottle/mic placements.



I believe the bipolar shifts in frequency response are caused by mixing of the incident wave with a "reflected" wave of the same frequency but with a slight phase shift. As the reactance crosses zero at resonance, this shifts from constructive to destructive interference. Like I noted earlier, this is not a quantitative measure of the absorption coefficient but it should give a qualitative depiction of the impedance. There is no point showing the corresponding curves for the MDF boxes, because they do absolutely nothing.

Here is a link to a video showing deflection of a candle flame by my large MDF box:

And another video showing the sound level around the mouth of a soda bottle as it is loaded with cotton balls:

.

I know this site is frequented (and run) by people who have much more audio engineering expertise than I do, and would be grateful for any help in interpreting these results and designing further experiments.

 

[Berwhale]

If you've not happened across it already, you may want to read the thread by @sarumbear regarding the Helmholtz resonators they're built for their HT... https://www.audiosciencereview.com/...ustically-treated-home-theatre-updated.36124/

 

[Delrin]

Thanks!

I had read through that thread earlier, and re-read it again tonight. I also downloaded and read through the Master's thesis that is linked in one of the posts.

It's clear a lot of thought went into the acoustic treatment, and that @sarumbear has some training in this area.

Here is what I was able to glean from the thread:

• there are five Helmholtz resonators, each made from 5m lengths of 25cm plastic water pipes (or around 16' x 9" in imperial); each targets a different frequency
• the resonator ports were rectangular openings, adjusted in size to achieve the desired resonant frequency - long "vents" were not used
• porous absorbent material for additional damping was not used

It is not indicated what frequencies were targeted (although 30-60Hz is mentioned), and because the treatment was built into the room there is no "control" data showing the specific impact of the Helmholtz resonators. The only room data shown is SPL magnitude vs frequency at three listening positions. The frequency response looks flat to within a few dB, but there are no waterfall plots or spectrograms (so it's hard to know what is happening in the time domain). There is a note that "No EQ is used" although the post mentions that a Trinov system (capable of room optimization) is included in the setup (presumably this was turned off for the FR measurement to isolate room treatment effects).

The setup looks really nice, but it is difficult to know what is the specific effect (if any) of the Helmholtz resonators. The room is fairly large, so one would assume the (untreated) modal peaks would not be as bad as in a bedroom-sized home studio.

This is a really interesting approach, particularly since such unusually large resonators are used. It also raises some interesting physics questions:

• in addition to their Helmholtz resonance, the tubes described can be expected to have strong "pipe resonances"; isn't there a risk that this will cause undesired acoustic effects?
• it seems like the total surface area of the resonator ports would be a tiny fraction of the room boundary area, and also very small compared with wavelengths in the 30-60Hz range that was mentioned. I am having a hard time visualizing the physics of how a single hole at the end of a pipe (even a large one) can have a significant impact on such large waves that are resonating between such expansive areas of wall.

In regards to the Master's thesis, it is really interesting reading and explains many things quite well. Much of the work describes simulations, but there is a really nice experimental section at the end where they build a custom impedance tube and demonstrate a reasonably good match with simulated absorption coefficients. It's also worth noting that all of the thesis work considers frequencies above 100Hz, whereas modal issues in small control rooms can be below 50Hz.

One thing I'm trying to understand is why only the absorption coefficient, but not the phase of the reflection coefficient, is considered in so many discussions of HR absorbers (the word "phase" only appears a couple of times in the entire thesis document). When we're looking at standing waves at these low frequencies, I would have thought that the phase would be quite relevant. Because of this, I'm having a hard time understanding the fixation on the (magnitude-based) absorption coefficient when we're talking about low frequency standing waves rather than a diffuse sound field. In the thesis, the student does acknowledge some of the limitations (including the fact that the COVID-19 pandemic made it impossible for them to do scaled up testing of their resonators).

For me, a "holy grail" would be a controlled experiment demonstrating the use of Helmholtz resonance to achieve measurable acoustic benefits in a small control room type of situation. Ideally there would be enough information provided so that someone could easily replicate the experiment. The approach described by sarumbear is intriguing, but I don't see that thread meeting this criterion (and to be fair that's not what sarumbear was setting out to do).

 

[Delrin]

I have made some progress in understanding how "neck geometry" can affect the performance of a Helmholtz resonator. I was inspired in part by this paper, which shows how sharp edges in resonator necks can lead to greater vortex shedding than when the ends of the neck are "chamfered".

This turns out to be easy to demonstrate experimentally. I made some resonators using ABS pipe, with a hole in one cap to serve as the "neck":

This makes it easy to vary the cavity volume and neck geometry. Below are some examples of different "necks" I've used:

Basically, I've found that HR necks having sharp edges, especially when combined with a long/narrow "aspect ratio" conducive to flow restriction, are very good at deflecting candles and very poor at influencing the local sound field. I think the candle deflection is analogous to "port chuffing" that is seen when a bass reflex speaker is driven above its practical operating range. Conversely, adding a chamfer to an HR neck, particularly when combined with a less restrictive "aspect ratio", seems to eliminate the candle deflection while greatly enhancing the acoustic reactivity (even keeping the resonant frequency constant).

Below are two spectrograms for an HR tube tuned to around 40Hz, in which the only difference is the addition of a chamfer on the inner and outer edges of the "neck":

In both spectrograms, you can see long tails associated with "pipe resonances" of the tube. When a chamfer is added to the neck hole, the decay tail at the 40Hz resonance is much more prominent - indicating that resonance is enhanced compared with the sharp-edged case. This is also evident in the frequency response curves, which show a much stronger "phase reversal" effect at the resonant frequency when the neck edges are chamfered. In keeping with the different resonance mechanisms, the neck geometry has very little effect on the "pipe resonances" that are also observed.

 

[Delrin]

Noting that chamfering, or "flaring" of the neck appears to improve the acoustic reactivity, I also built a larger resonator that is very reactive:

Here are frequency response curves comparing a flat pipe cap with a chamfered 3/8" hole versus the larger assembly using a series of flared pipe couplers:

The cyan/blue curve is the flat cap with chamfered 3/8" hole, while the orange curve is for the flared assembly with a 1.5" diameter neck (4.5" long). The green curve is a "control" where the pipe was flipped around to present the back end to the measurement mic.

Adjusting the length of the 1.5" diameter "neck" in 1/2" increments allowed the resonant frequency to be tuned easily:

and the very strong resonance in the "flared" configuration is evident from the spectrogram:

As in previous examples, all measurements are done by "close micing" around the mouth of the resonator.

I want to stress that the purpose of this exercise is just to demonstrate Helmholtz resonance at 45Hz and it's unclear whether this construction would have any value in a practical absorption scheme for controlling a room mode. The acoustic effect is very localized to the mouth of the resonator, and I can not see this influencing the overall room acoustics in any significant (or useful) way.

The way I am picturing absorption from this resonator is that, when it is excited by an incident wave at the target frequency, a phase-reversed wave is emitted from the mouth. This causes partial cancellation of the incident wave, but the amplitude of the phase-reversed wave falls off rapidly with distance away from the mouth so the attenuation is very localized for a single resonator.

 

[Vladimir Filevski]

Impressive effort by @Delrin! Thanks!

Helmholtz resonators are enticing for the control of low frequency room modes, and it's remarkable that such small structures can resonate at such low frequencies. However, they seem to have been largely written off by the audio community because they so often fail to perform as expected (there are many online accounts where considerable effort is devoted to building an HR absorber that seems to do nothing at all acoustically).
...

Helmholtz resonators must have enough mouth/throat area and they must contain damping material in the cavity volume, to be effective.

I am starting by looking at the behaviour without any absorbent material in the cavity, as the physics are more predictable and easy to interpret.
...
Here are some MDF boxes made from 3/4" MDF. The cavity size for the two small boxes is 4x4" with a depth of 7.25" for the smaller box and 12" for the longer of the two "single cell" boxes. The larger box is 6' tall x 22" wide and also has 1/4" holes in 3/4" MDF, with a cavity depth of 7.25" and a hole spacing of 4" centre-to-centre. .... They do exhibit resonance at this frequency, but only via the "candle deflection" test. They have no acoustic effect at all, either on the room or right at the mouth of the resonator cells.

Even the big HR box (6'x22') with 85 holes (if I counted them right) with 1/4" openings has total mouth/throat area of only one 2.3" hole! That is not enough!
For a client with very problematic room acoustic (perfect square room with two very prominent resonances at 35 Hz and 70 Hz) I built two damped HR boxes (using existing furniture boxes, emptied of the usual content), each box tuned to the corresponded frequency (35 or 70 Hz) with two PVC pipes with about 3" diameter. The result? Only 2 dB absorption and moderate improvement of the waterfall diagram at the two room resonances. Sadly, there was no space in the room for additional Helmholtz resonators.

And another video showing the sound level around the mouth of a soda bottle as it is loaded with cotton balls:

.

This video is a perfect example that always there is an optimum amount of damping material inside the HR box, to be most effective.

 

[sarumbear]

For me, a "holy grail" would be a controlled experiment demonstrating the use of Helmholtz resonance to achieve measurable acoustic benefits in a small control room type of situation.

As you surmised I have studied the subject of acoustics at a high level and I have the means to access to capable acoustic simulation software during architectural design. This allowed me to visualise and counterattack acoustics of the room that I want as a living space first, listening second. When the room was built it was within a few dB and milliseconds of the simulation. This was totally expected as I believe in simulation.

The way we design have changed. The days of testing are gone and software simulators took its place. Car companies have stopped building clay models for instance. Can you imagine testing billion+ transistor ICs via experimentation?

Ideally there would be enough information provided so that someone could easily replicate the experiment. The approach described by sarumbear is intriguing, but I don't see that thread meeting this criterion (and to be fair that's not what sarumbear was setting out to do).

My thread was meant to show that purely acoustical treatments (including room layout design) will achieve a flat room response and consistent RT60 through out the audible range. Acoustics is an architectural discipline. Correcting bad room acoustics is rather like applying band-aid to a wound. As I had the means and the opportunity to build a house I simply used my education.

As a note to EQ: I have only used EQ to tame the frequencies in the earlier incarnation of the room where I was using only three resonators. Later I added the two resonators that was missing from the original design and the EQ was no longer needed. I have however still used EQ but mostly above 500Hz.

 

[Delrin]

Impressive effort by @Delrin! Thanks!

Thanks Vladimir!

Helmholtz resonators must have enough mouth/throat area and they must contain damping material in the cavity volume, to be effective.

Agreed - it seems intuitive that, regardless of the size of the resonator cavity, the relevant "surface impedance" is presented at (and only at) the mouth of the resonator. A (1,0,0) room mode will have an associated zone of maximal pressure that spans the entire back wall of the room (which might be 100 square feet even in a small room). At low frequencies/long wavelengths, this maximal pressure zone tapers off rather gradually (co-sinusoidally) as you move away from the wall. That is a lot of (slightly) pressurized air! This is why I have difficulty visualizing how "discrete" resonators with a single mouth are sometimes described as being capable of "cancelling a room mode".

In regards to the need for damping material, there are still aspects of this I am trying to grasp. On the one hand, it does make intuitive sense to add damping when considering the Helmholtz resonator as a driven harmonic oscillator. On the other, a resonator without any added damping can exert considerable phase cancellation at frequencies that are slightly above resonance (more on this below). I have noted above that I remain puzzled by the focus on "absorption coefficient" in the modelling of Helmholtz resonators. Absorption coefficient is simply one minus the squared magnitude of the complex reflection coefficient (phase information is discarded). It's a concept that makes sense when applying a statistical model of the diffuse sound field to porous absorbers at higher frequencies, but I'm skeptical about this approach for modelling explicit wave phenomena like low frequency room modes interacting with Helmholtz resonators.

Even the big HR box (6'x22') with 85 holes (if I counted them right) with 1/4" openings has total mouth/throat area of only one 2.3" hole! That is not enough!
For a client with very problematic room acoustic (perfect square room with two very prominent resonances at 35 Hz and 70 Hz) I built two damped HR boxes (using existing furniture boxes, emptied of the usual content), each box tuned to the corresponded frequency (35 or 70 Hz) with two PVC pipes with about 3" diameter. The result? Only 2 dB absorption and moderate improvement of the waterfall diagram at the two room resonances. Sadly, there was no space in the room for additional Helmholtz resonators.

Yes I'm not sure I seriously expected the big boxes to "work", but they are typical of DIY efforts and I wanted to understand what they are actually doing (or not doing). The total surface area of the holes is indeed tiny, which seemed intuitively like a limitation. I suppose there could (very hypothetically) be circumstances where there is mutual interaction between the holes in the array that enhances their effect. For example, if we consider them as an array of point sources for phase-inverted hemi-spherical wavefronts that tend to (very partially) cancel the modal wave, then this could in theory provide a mechanism of action. In practice, the neck geometry seems to be so bad that the holes are mainly good for snuffing out candles - without any apparent interaction with the local sound field (I replicated this using equivalent ABS tubes mated with carefully machined plastic necks and got very similar results).

This video is a perfect example that always there is an optimum amount of damping material inside the HR box, to be most effective.

Thanks! That video is actually part of a series of measurements I took that also demonstrates nicely the "phase reversal" effect around the resonant frequency.

The plot below shows the same experiment, with the frequency increased to 225Hz (25Hz above the resonant frequency of the bottle):

In this case, there is a strong attenuation of the SPL around the mouth that is maximized when there is no damping in the bottle. The effect is entirely due to destructive interference cause by a phase-inverted wavefront emitted around the mouth of the bottle. The effect is progressively diminished as more cotton balls are added (each successive dip in the plot corresponds to the addition of five cotton balls).

My main motivation in doing all this is that there is some great physics to be learned!

 

[Vladimir Filevski]

That video is actually part of a series of measurements I took that also demonstrates nicely the "phase reversal" effect around the resonant frequency.

The plot below shows the same experiment, with the frequency increased to 225Hz (25Hz above the resonant frequency of the bottle):

In this case, there is a strong attenuation of the SPL around the mouth that is maximized when there is no damping in the bottle. The effect is entirely due to destructive interference cause by a phase-inverted wavefront emitted around the mouth of the bottle. The effect is progressively diminished as more cotton balls are added (each successive dip in the plot corresponds to the addition of five cotton balls).

Yes, the attenuation of empty HR is maximal slightly above the resonant frequency, but it introduces amplification at the resonant frequency - which must be avoided.
There is a good compromise - damped HR box with not so big attenuation, but also without the amplification of resonance. I can not stress enough the importance of finding the optimal amount of damping material.

 

[Delrin]

Thanks for the reply sarumbear!

As is probably clear by now, this thread is mainly about my didactic interest in poking around the physics of Helmholtz resonant absorption. I've worked for many years applying other types of resonance phenomena and find that it's fun and educational to try and understand how similar physical concepts are used in different fields and applications. I have taught graduate engineering courses on subjects ranging from linear systems theory to biomedical ultrasound, but architectural acoustics is something completely new to me. If I can really get my head around Helmholtz absorption, there could be some nice material for future teaching activities.

As you surmised I have studied the subject of acoustics at a high level and I have the means to access to capable acoustic simulation software during architectural design. This allowed me to visualise and counterattack acoustics of the room that I want as a living space first, listening second. When the room was built it was within a few dB and milliseconds of the simulation. This was totally expected as I believe in simulation.

The way we design have changed. The days of testing are gone and software simulators took its place. Car companies have stopped building clay models for instance. Can you imagine testing billion+ transistor ICs via experimentation?

I work in a university, and have access to academic licensing terms for many types of modelling software (and a discretionary budget for purchasing software if it really seems useful). Might I ask what packages you have used or recommend? I have used OpenFOAM (computational fluid dynamics, although can do some acoustic modelling) and at some point was considering a trial period for COMSOL with the acoustics package. Ansys is also free for academic institutions, although it is Windows-only (we are mainly Linux/Apple). We use CST quite extensively for electromagnetic SAR modelling (on a dedicated Windows host with a $20k GPU), but we also do extensive experimental validation for regulatory and safety reasons (so I'm familiar with the use of physics modelling software).

Despite the power of modern simulation software, I still believe it is important to have both an intuitive grasp and theoretical understanding of the phenomena being modelled. The effect of vortex shedding in Helmholtz resonators is a good example - classical modelling of linear effects can do a good job of predicting the resonant frequency, but it won't tell you about non-linear effects from a crappy neck geometry that completely trash the impedance model.

I completely believe you that large companies will have mastered the use of simulation software and apply this daily to design Helmholtz absorbers for exhaust pipes, jet engines, and other automotive applications. However, this is no doubt built on a solid foundation of understanding the problem domain and there seems to be a disconnect between the popular understanding of Helmholtz resonance and its successful application in sound absorption. I know from personal experience that the simulation pipelines used in industry are built on the back of a lot of hard work in setting up the problem space.

This thread was meant to show that purely acoustical treatments (including room layout design) will achieve a flat room response and consistent RT60 through out the audible range. Acoustics is an architectural discipline. Correcting bad room acoustics is rather like applying band-aid to a wound. As I had the means and the opportunity to build a house I simply used my education.

I agree completely that there can be no competition with a space designed, from the ground up, with acoustic performance in mind. Your thread demonstrates this very nicely.

The scope of the current thread is on understanding the physics of Helmholtz absorption at an intuitive and theoretical level. For me it is primarily an educational undertaking, but one that could also be of practical interest for readers whose unfortunate rooms are like gaping wounds that require some form of treatment. The apparent potential of Helmholtz resonators for "cancelling room modes" would seem to make them particularly relevant to those most in need. Due to the realities and economics of real estate, there are many situations where academic and commercial sound engineering is subject to space restrictions.

As a note to EQ: I have only used EQ to tame the frequencies in the earlier incarnation of the room where I was using only three resonators. Later I added the two resonators that was missing from the original design and the EQ was no longer needed. I have however still used EQ but mostly above 500Hz.

Thanks for clarifying that!

I would be interested in replicating one of your resonators for further experimentation. If I understand correctly, they are made from 5 metre lengths of 25cm-diameter plastic pipe. I assume that ABS piping used for drainage would be ok, and that a standard ABS pipe cap could be used to close one end. Depending on the requirement for "neck length", the other end could be implemented in a couple of ways. One would be to use another ABS pipe cap with a round or rectangular hole (the material would be around 5mm thick - which would constitute the neck length). Alternately, one could machine (or 3D print) a thicker plug out of plastic or MDF to get a longer neck length if required.

Any implementation details that would help replicate your resonators would be greatly appreciated!

 

[Delrin]

Yes, the attenuation of empty HR is maximal slightly above the resonant frequency, but it introduces amplification at the resonant frequency - which must be avoided.
There is a good compromise - damped HR box with not so big attenuation, but also without the amplification of resonance. I can not stress enough the importance of finding the optimal amount of damping material.

Thanks!

Could this not be exploited in a (1,0,0) mode where there is a strong roll-off below the fundamental frequency? One could tune the resonator to a frequency slightly below the modal frequency, so that the modal peak would span the range of attenuation due to phase reversal.

I had also noted that @sarumbear's resonators did not appear to contain any damping material, but were purported to be effective in addressing room modes.

Of course all this is moot if the resonator does nothing to the room due to insufficient area coverage...

 

[sarumbear]

Helmholtz resonators must have enough mouth/throat area and they must contain damping material in the cavity volume, to be effective.

Agreed.

In order to make a Helmholtz resonator absorb sound, instead amplifying, you need to slow the air oscillating in the opening by friction. I glued a thin fleece material to the rear of the opening with an additional layer of wool behind it.

Similar but opposite in action of subwoofers, the amount of energy to absorbed can only be generated with equally large amount of air displaced, I.E. with large opening area.

 

[sarumbear]

Might I ask what packages you have used or recommend?

Anything that requires simulation of a physical phenomena I suggest using Wolfram Mathematica.

Here is what Wolfram gives as an example. Imagine what can be done by using a custom front end and using the actual architectural model of the room that the builders used to build it.

 

[DonH56]

I have had limited exposure to various SW packages just for "fun" as this is not my day job. In addition to Mathematica:

• COMSOL is another software package good at flow modelling and such and has been used for acoustic analysis.
• Matlab is available but AFAIK does not have a good acoustic toolbox; there are third-party add-ons available, with various levels of support, so you usually need to know what you're doing to use them.
• There are a number of Python packages available, again good for analysis, less so for teaching and understanding the underlying theory.

As @sarumbear said, the problem for most of these is getting a reasonable front-end to feed the solving engine, and how to do that is not always obvious or easy to do. Ditto the back end, though plotting packages can do most anything these days -- once you figure out how to use them to provide meaningful results and not just pages of pretty (and often very busy) pictures. I claim no acoustics expertise with any of these programs -- I have used them all but for different (non-audio) applications. For high-level analysis, COMSOL and Mathematica are probably best IME/IMO, albeit with a higher price tag and perhaps steeper learning curve.

An interesting twist on resonator structures is to use membrane absorbers, thin panels with small openings specifically designed to absorb specific frequencies. You can put a lot of different holes (resonators) in a 2' x 4' x 1" or whatever panel to achieve broadband absorption well into the bass region, or tailor the panel to squash specific room modes. There are a few commercial versions and some papers to DIY.

HTH - Don

 

[Delrin]

Anything that requires simulation of a physical phenomena I suggest using Wolfram Mathematica.

Here is what Wolfram gives as an example. Imagine what can be done by using a custom front end and using the actual architectural model of the room that the builders used to build it.

Thanks! I haven't used Mathematica in years, but it was actually the first maths package I ever used in the early 1990's and it was very inspiring. The example you linked to is very nicely laid out, and I'll explore this further. Happily we have a free site license for Mathematica where I work.

Matlab is kind of an industry standard in my domain, but I can tell you right off the bat that the Wolfram room mode tutorial is way better than any acoustics examples provided for Matlab (which actually has excellent examples across a wide range of domains - it's just a bit thin on acoustics for some reason).

I had not realized that Mathematica had such rich support for physics modelling, so thank you for the information!

 

[Delrin]

I have had limited exposure to various SW packages just for "fun" as this is not my day job. In addition to Mathematica:

• COMSOL is another software package good at flow modelling and such and has been used for acoustic analysis.
• Matlab is available but AFAIK does not have a good acoustic toolbox; there are third-party add-ons available, with various levels of support, so you usually need to know what you're doing to use them.
• There are a number of Python packages available, again good for analysis, less so for teaching and understanding the underlying theory.

As @sarumbear said, the problem for most of these is getting a reasonable front-end to feed the solving engine, and how to do that is not always obvious or easy to do. Ditto the back end, though plotting packages can do most anything these days -- once you figure out how to use them to provide meaningful results and not just pages of pretty (and often very busy) pictures. I claim no acoustics expertise with any of these programs -- I have used them all but for different (non-audio) applications. For high-level analysis, COMSOL and Mathematica are probably best IME/IMO, albeit with a higher price tag and perhaps steeper learning curve.

An interesting twist on resonator structures is to use membrane absorbers, thin panels with small openings specifically designed to absorb specific frequencies. You can put a lot of different holes (resonators) in a 2' x 4' x 1" or whatever panel to achieve broadband absorption well into the bass region, or tailor the panel to squash specific room modes. There are a few commercial versions and some papers to DIY.

HTH - Don

Thanks Don,

I've used Matlab for many years and it is great but for some reason it does not seem to be the platform of choice in academic acoustics research (which is not my domain).

It's worth mentioning that Trevor Cox, co-author of the classic book "Acoustic Absorbers and Diffusers: Theory, Design and Application" has posted code for many of the book examples in the Matlab File Exchange (link here).

I am interested in COMSOL as well, as it is dedicated to PDE solutions, but even the academic licensing is rather expensive and I've heard mixed reports on it. I'm negotiating a trial license with their regional sales rep, and will probably set this up when I have time to give it a proper go.

I'm also using OpenFOAM, which is freely available and very powerful for both linear and non-linear problems. It is actually not bad, despite lacking a fancy GUI, and is pretty intuitive and has the benefit of being widely used in academia.

Thanks also for the tip about membrane absorbers... that is my next project lol.

 

[Delrin]

Yes, the attenuation of empty HR is maximal slightly above the resonant frequency, but it introduces amplification at the resonant frequency - which must be avoided.
There is a good compromise - damped HR box with not so big attenuation, but also without the amplification of resonance. I can not stress enough the importance of finding the optimal amount of damping material.

FWIW, here are some frequency response curves I obtained for the 4" pipe resonator, assembled using flared couplers to transition down to a 1.5" neck of 4" in length (see photo above).

The curves include a "control" (back side of the capped tube), as well as the empty resonator followed by iterations in which 100 cotton balls were dropped into the cavity. The mouth of the resonator was presented to face the single active monitor at a distance of around three feet, with a flat measurement mic placed just outside the mouth at a 45 degree angle.

You can see that the impact of the progressive damping on the HR phase reversal. Interestingly, the pipe resonances go away almost immediately after very little damping. The Helmholtz resonance requires a lot more damping to attenuate it.

For completeness, here is a plot showing all the iterations I did with increments of 20 cotton balls.

In the unlikely event that anyone finds this extremely fascinating, I would be happy to share the mdat file (please remind me of the trick to allow uploading files of this type onto the forum).

 

[Geert]

In the unlikely event that anyone finds this extremely fascinating,

I do for sure, but I'm still breaking my head over the effect of the flared pipe couplers. Is it the flaring that matters, or did the resonator become more effective because it increased in length.

 

[Delrin]

I do for sure, but I'm still breaking my head over the effect of the flared pipe couplers. Is it the flaring that matters, or did the resonator become more effective because it increased in length.

I am pretty confident that it's the flaring that helped. My working hypothesis is that messy airflow around sharp corners will contribute small, non-linear effects that cause the system to depart from an ideal "mass-spring" system. Anything that alleviates restricted or turbulent flow will improve the "quality" of the resonance.

I suspect that there is an important difference between "linear" resistive losses that are introduced intentionally by adding a porous absorber for damping, versus "non-linear" effects that are associated with turbulent airflow around the neck.

Here is a telling figure from the Förner et al paper I referenced above:

In their paper, the neck size that was tested required a relatively high SPL for the air movement to depart from linearity around the neck. My crude test results (with the candle) suggest that similar effects can arise at lower SPL in the specific neck geometry I was using.

In Figure (a) for the sharp edge, you can see that there is an "air jet" directed along the axis of the neck (and this is noted in the text, which can be downloaded from the link above). These are non-linear effects that require very specific simulation techniques to model (techniques which would not be used or necessary for modelling - say - room modes).

It is worth mentioning again that the emergence of these effects above some SPL threshold is what causes "port chuffing" in a ported speaker when it is played too loud.

 

[Vladimir Filevski]

You can see that the impact of the progressive damping on the HR phase reversal. Interestingly, the pipe resonances go away almost immediately after very little damping. The Helmholtz resonance requires a lot more damping to attenuate it.

Yes, that is exactly the same result I obtained - low to moderate effectiveness of a single HR box for LF absorption. For good results, it require big volume(s) devoted to HR box(es) - very limiting in a typical living room.