Helmholtz Resonators Questions For The Experts

[Strabo]

Dr. Who's EOH thread started me researching these things and I found a formula online to use to calculate the resonant frequency.

=(v_of_sound / (2*PI())) * (SQRT(Area / (Volume * Length)))

I plugged that into Excel and started playing. What I noticed was that the diameter had no effect on the frequency when using a cylinder. The math makes sense because 'Area' in the formula above would be canceled out by part of the volume formula.

So for a cylinder you could rewrite the formula as

= (v_of_sound / (2*PI())) * (SQRT(1 / Length^2)). No problem.

But in my mind volume has to have some affect. Does the volume of the resonator correlate at all to the decibel decrease at the resonant frequency? If so, by how much and can that be factored in to get the desired effect?

How narrow a band does a Helmholtz resonator affect? Is it just that one frequency? Or does it have a width of +/- something? I would think the width if it existed would be derived from the frequency but then at what amount of roll-off?

Definitely more research is needed on my part but I thought I would pose some questions here so we can all learn.

[DrWho]

The larger the surface area of the mouth of the resonator, the more impact it is going to have at that frequency. You can imagine that a long straw in the room would really have no effect - and that's cuz the mouth isn't very large. I also think the tube loses its resonant effectiveness when the length is shorter than 1.5 the width of the mouth. For example, an adjacent room or bay window, etc etc...I'm sure there's an exact number, I just don't know what it is. There's probably some way to calculate the most efficient mouth diameter for a given length.

Btw, here's an even simpler formula for those that want the size of their tube in feet:

frequency = 360 / Length

Or if you want to calculate the length for a given frequency:

Length = 360 / frequency

[]

[westcott]

Dr. Who's EOH thread started me researching these things and I found a formula online to use to calculate the resonant frequency.

=(v_of_sound / (2*PI())) * (SQRT(Area / (Volume * Length)))

I plugged that into Excel and started playing. What I noticed was that the diameter had no effect on the frequency when using a cylinder. The math makes sense because 'Area' in the formula above would be canceled out by part of the volume formula.

So for a cylinder you could rewrite the formula as

= (v_of_sound / (2*PI())) * (SQRT(1 / Length^2)). No problem.

But in my mind volume has to have some affect. Does the volume of the resonator correlate at all to the decibel decrease at the resonant frequency? If so, by how much and can that be factored in to get the desired effect?

How narrow a band does a Helmholtz resonator affect? Is it just that one frequency? Or does it have a width of +/- something? I would think the width if it existed would be derived from the frequency but then at what amount of roll-off?

Definitely more research is needed on my part but I thought I would pose some questions here so we can all learn.

My only problem I have with suggesting HR's is that due to the narrow frequency they address, you have to make sure that it is fixing the problem frequency.

Room calculators are convenient but without actual in room measurements with the proper equipment, you could go to a lot of trouble and not address the proper frequencies, IMO.

[Strabo]

I downloaded 1hz test tones I think from Real Traps (don't remember).

Using that I narrowed down issues that matched the standing waves calculations of 27hz, 52hz, and 72hz based on readings and room dimention calculations.

At this point I'm not to worried about the 27hz because my speakers barely put out sound at that level. I don't use a sub for music but I will use my parametric eq for the sub for movies which isn't as important to me.

I have a peak at the listening position at 52hz which with some speaker placement and some tubing I was able to knock 1 db off and widen the peak a few hz.

My biggest problem is at 72 hz. Actually, it's 75hz +/- 3hz. I have about a 6hz section in the 70's (72hz - 78hz) that is sucked out, down 7db. I was able to add back 1db from 75-78 with the tubes I made yesterday. This doesn't seem to be a harmonic of the previous problem frequencies, and does tie to the 7' 9" ceiling standing wave calculation. If I could get half of this back I would be happy as punch.

Any suggestions?

Also, any information on my previous question of how tight HR's work? Is it exactly the calculated frequency or is the +/- a couple percent?

Thanks for the suggestions.

[mas]

I apologize in advance for not having the time to address this right now with the thoroughness it deserves, but I think a better understanding of room modes is necessary here before you waste time and energy.

First, the room mode calculator. Is your room a perfect rectangle? Does it have any open doorways, alcoves, or ANY irregularities or adjoining spaces? If so, the calculator is a computer game and not an accurate representation of what is happening in your room. Oh, it can give you a few ideas of what may be happening, but not enough for you to surgically treat problems.

Lacking more sophisticated measurements, you would do better with an SPL meter and canvasing the room. (Lots of fun...and how much time do you have?)

Also, you are not going to EQ your way out of resonance issues.

Helmholtz resonators are fascinating creatures, and there is not just one type or design. And all are precisely tuned. So, as mentioned earlier, they are specific answers to specific problems.

Let me back up and begin to present a very simple explanation that more would do well to pursue. Many are familiar with impedance in an electrical system.

Well, here we are literally dealing with acoustical impedance. Energy is stored and released in the system. That means there is both kinetic and potential energy that is present. To jump to the chase without fully addressing all of the issues, in a system, the source of energy exhibits a particular complex impedance that varies with frequency and time. Sorry, but the old "8 ohm" etc. nominal impedance nonsense doesn't cut it any more. A load that matches the source impedance precisely will absorb all of the energy perfectly. There is no reflection of energy back into the system.

A system where the load does not perfectly match the source impedance results in reflections of energy back into the system. And a room with its surfaces exhibits precisely this very complex behavior. The shape and the surfaces each have characteristic impedances, and as a result LF establish standing waves, just as in a tuned open or closed pipe (the only difference being in an open pipe you have an anti-node and in a closed pipe you have a node.)

As you approach wavelengths that are smaller than the room, you have specular reflections that are treated with absorption and diffusion. And absorption works only at certain frequencies and acts as a reflector at other frequencies - precisely because it too exhibits an acoustical impedance that matches only part of the system energy - and where its impedance is not sufficiently equal, it reflects energy back into the system.

Likewise, with diffusion, we now use the more sophisticated quadratic residue sequence calculations and other models based upon fractal, chaos and power laws based upon the concept of self-symmetry (see Manfred Schroeder's works and resultant applied products such as those by RPG) to model and control the reflections of radical impedance mismatches in an attempt to reflect and diffuse the specular reflections.

But back to the Helmholtz resonator. Properly tuned, it too acts as a terminator.

Just like in an electrical system of, say your local cable system...If you have a second TV set, and you disconnect it and simply leave the wire unterminated, you will get reflections in the system due to the unterminated line and you will get ghosts and standing waves - interference - in your other set. This is solved by terminating the open line with a barrel and a 'terminator cap that is essentially a cap with a 75 ohm resistor that shorts the line, effectively terminating and absorbing the energy at the characteristic impedance that is transmitted to it.

Well, this is also what a Helmholtz resonator does to a particular frequency standing wave. It acts as a matched terminator that absorbed the tuned energy at a particular frequency and prevents its regeneration back into the room system.

And as alluded to earlier, the most simple and classic model is the tuned pipe - a tube trap. But there are many styles of Helmholtz resonator. Some are simple and some are amazing complex, but all do exactly the same thing. They act as a terminator absorbing the energy at a particular frequency by resonating at precisely that frequency.

And while I realize that this is a very basic description that would benefit greatly by a much deeper analysis, I hope that it helps to make the basic concept apparent - or at least can point you in a more productive direction. The only other real suggestion at this point that I would make is to steer away from the idea of solving this problem with EQ. The source of the problem is not whether the direct source signal has that frequency or not!

Oh, and I almost forgot, the notion that you can ignore certain frequencies in treating standing waves is convenient, but fundamentally flawed! You are dealing with harmonics - multiples of a fundamental frequency. The low frequency standing waves are not generated simply as a result of your source material, but as a function of the geometry of the room! Oh, you can try to focus on one at the expense of ignoring the other multiples, but you will soon find that your efforts are less than you hoped! You would do well to address the fundamental frequency!

Well, gotta run for now...Hope this helps a little. (This is where its appropriate for you to say "Huh? What did he say?")

[DrWho]

Any suggestions?

Ideally...get some measuring equipment []

But since you're doing this by ear, I've got a few ideas you might try. First, as Mark pointed out, ignore the frequencies calculated in the room mode programs. I've found that they give you a good idea of where to look, but you're gonna be better served accepting that the actually frequency should be at a different frequency (unless your room is a perfect rectangle with no furniture in it). This is way incredibly easier to do if you can use a device that sweeps frequencies instead of limiting yourself to 1Hz increments. Got a computer handy?

Once you find the offending frequencies, run around the room with the fundamental frequency playing and measure the SPL at various positions throughout the room. You'll need to measure in all three dimensions - don't forget that height plays a roll too. Anyways, what you're looking for are spots in the room where the biggest peaks occur. And then you'll want the mouths of the helmholtz resonators at the locations of these loudest peaks. You might also want to double check the locations of your peaks with harmonics of the fundamental. In other words, start measuring the 27Hz issues and make a list of locations that might work (since it's usually along the walls/corners, I just put a little X on the wall with the SPL measurement beneathe it). Then check every location with ~52 Hz. Pick the locations that are similar to both.

Then, when placing the helmholtz resonator, stick your head where the mouth of the tube is going to go, but hold the tube away...play some bass heavy music and then pull the tube towards the spot that it needs to go. If everything is working right, you'll hear the boominess drop out when the tube is in position. It's pretty cool actually. If you don't notice any drop, then something problem isn't working - probably a tube that's working at a different frequency. If the tube doesn't work and you've got a friend handy, you can try changing the depth of the tube until you hear the boominess go away. This is pretty easy to do with sonotube and a wood circle cutout that just fits inside - cut the tube too long and then slide it up until you achieve the attenuation you desire.

The actual formulas used for calculating the tube lengths are overly simplified so some amount of attenuation may be needed. Things like the humidity and temperature in the room are going to affect the velocity of sound in your room, which is going to change the effective resonance of the tubes - which means you may be doing everything "correctly" but the length of the tube is incorrect as a result...

Btw, I'd love to see some pics of your experimenting.

[Strabo]

I'll be in and out today since I'm in an Access training class all day. [:S]

Some background that I left out. I'm trying to fix these issues as inexpensively as possible so I don't have a lot of equipment at my disposal. I do have a Rat Shack meter and the test tones and that was used to take readings. It wasn't soley base on the room measurement equations. I used the equations as a starting point then took readings with pretty much confirmed the equations.

The room is not at all square and I will post the dimension and room setup in the next post.

Off to class.

[mas]

I sure hope that I do not sound 'flip' here...but I think we are going in circles.

I completely understand your desire to address this issue. And this is the primary aspect of room tuning that everyone should address. It is fundamental before any other aspects are addressed.

But we are limited by physics. The only way a room mode calculator comes even close in predicting room modes is that the room is a perfect rectangle. And no real world room is. This model neglects doors, surfaces, lights, everything...and none of use have such a room. Building Codes do not allow it.

All variations from this ideal significantly complicate the process and cause deviations.

And the tuning of Helmholtz resonators is sufficiently precise (although you can make some that are lower Q that perform OK (but less efficiently) over a broader bandwidth) that you need measurements in order to surgically apply them. Thus posting pictures will not make it any more effective in making judgments about how to apply them. The general guidelines will still be valid. If the room is enclosed, all of the modes will converge in the corners of the room. If the room is open on one end (as in a room that opens into an adjoining large space such a great room, they will not - and also the coupled space will cause the modes to change...just as all irregularities will.

So, bringing us back again to the beginning. Measurements are necessary to identify the individual frequency peaks and their Q. Their location is helpful as well. Calculators are useful only in giving us an indication that they do indeed exist. Measurements tell us what actually exists and where. ..And to think that this is one place where an RTA is actually useful!

From the measurements we can suggest specific designs for the various configurations of traps. But without them, we are merely speculating regarding the various general options that exist, not on a specific treatment. And Mike has already spoken to the trial and error method of addressing the issue.

[Strabo]

I sure hope that I do not sound 'flip' here...but I think we are going in circles.

I don't think you were being flip at all. I appreciate the input. The point here is for me and hopefully others to learn.

I gave in and downloaded the software from Home Theater Shack and have a new sound card on the way. That and 30 some feet of RCA cable should get us better information. We can start over when I have some graphs and figure out a way to draw up the room.