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FLINT: Standing waves and room acoustics


Prodigal Son
I have been putting off writing about acoustics issues with bass for a reason: it is a difficult subject to really get. However, once you get it, the topic seems intuitive and simple.

In most rooms there are at least two large opposing parallel reflective surfaces, like the walls, ceiling/floor, etc. These surfaces reflect sound back and forth with and can set up resonances between them at frequencies where the distance between the two surfaces are equal to the wavelength, or multiples of the wavelength, of the frequency being generated in the room.

Below is an example of a primary standing wave node where the distance between two reflective surfaces is equal to one full wavelength.


The red area is where the sound from the acoustic energy is the strongest and the white area is where the energy is the weakest. The highest energy point is called the antinode and the weakest is the node, or often the null. If you are standing exactly where the null is, there is absolutely nothing you can do electronically to make that frequency heard. Increasing the output level will make the red areas, the antinodes, louder, but the nodes (nulls) will remain absolutely silent to the ear as there is no energy at that point in the room.

However, if you are standing 3/4 of the way across the room, at the antinode point, the sound will be the loudest it can be at that frequency. if you boost that frequency to solve silence of the node, you will be boosting the antinode correspondingly. If you attempt to eliminate the antinode by cutting the frequency electronically, you will likely be forced to cut it completely and ensure you will never hear any content at that frequency on that system.

When acoustic energy is generated in a room, the inherent resonances the standing waves (called standing waves becase the nodes do not move through the room but are stationary) will start to build up at the exact frequencies where the wavelengths between the reflective surfaces is equal to the distance between the surfaces. So, if the walls in a room at exactly 20 feet apart in the example above, then the standing wave shown in that example is 56.5Hz. If you are standing exactly in between the walls and played a 56.5Hz sine wave test tone, you would not hear the primary wave (though you would hear some harmonics and other distortions and room noises).

That's at root single wavelength frequencies. What about other frequencies?

Well, the same rule applies to multiples of the standing wave frequencies. For instance, if there is a standing wave at 56.5Hz, then there will also be a standing wave at 113Hz, or two wavelengths in a given distance. The image below illustrates a two wavelength standing wave:


Again, if you are standing directly betwen the two surfaces, or the node point, then the root frequency will be inaudible. If you are standing at the 3/4 point between the walls, you are standing at another node, or null. Unlike the root standing wave where the 3/4 point is the absolute loudest, the 2 wavelength standing wave will have a null at the 3/4 point.

So, where would you want to be standing to get the most even bass?

Keep in mind that all multiples of the root standing wave will have strong nodes and anti nodes in the room. So, not just the single wavelength, but the two wavelength, three wavelength and four wavelength frequencies will all have standing waves up to the point where the room decor and other reflective surfaces start breaking up the acoustic waveform. So, in our imaginary sample room which has two large reflective walls which are 20 feet apart, you will have serious nodes and antinodes at 56.5Hz, 113Hz, and 169.5Hz. At 169.5Hz there will be 6 nodes, or nulls, spaced evenly across the room between the two surfaces.

This is simple two surface issues. Most rooms have six reflective surfaces in parallel pairs, so you have to deal with multiple standing wave issues all at the same time. So, if your head is placed directly in the center of the room, between each of the three reflective parallel sets of surfaces, you will be exactly at the node point for 3 sets of root standing waves plus all their multiples.
Have you ever blown into an empty drink bottle and made it whistle, or "hum"? That tone is the inherent resonance of the enclosed space inside the bottle. I am not going to talk about the inherent resonance of a large room, but I am going to talk about the way resonances carry on.

When you blow over a bootle top, it takes a second to get the resonance to start sounding out. Then, after you stop blowing the resonance continues for a moment as it slowly fades away. The same thing happens with resonances in our listening rooms. It takes a short moment to excite the resonance, but then it lingers after the excitation is removed.

You may have also noticed you can tap the opening of a bottle with your hand or finger and the resonance will also ring out for a short time after that impact. Again, the same thing can happen in our listening rooms where a short impact or "thud" can cause the room to resonate.

If all the surfaces in our listening rooms were solid concrete and there were no gaps for air to escape from, the resonances, once excited, would take a very long time to dissipate. In such a lossless room a resonance could, in theory at least, last for a hours or days as the energy has to dissipate somewhere (or be lost through some conversion). In the real world our rooms typically do not have solid concrete walls, floors and ceilings and they are definitely not completely sealed up and air tight. So, the resonances do not last forever.

However, our rooms are not completely lossy either. Standard stud frame & sheetrock walls have some inherent losses built into them which we rely on to keep our houses comfortable, acoustically, to live in. But the losses are not perfect, and they hve fixed frequencies based on the thickness of the sheet rock and the distance between the studs. At certain frequencies the sheet rock can be energized and vibrate wildly, storing the acoustic energy like a flywheel and return it to the room with more sustain than we want.

This sustain in the bass, cause by natural wall distance resonances and by the construction materials used in our homes, can be problematic. This is why serious audio nuts and recording studios, even architects designing large public areas, apply bass traps, or bass energy absorbers. Controlling the bass sustain will not only improve the inherent issues caused by a highly resonant room (all typical homes are extremely resonant in the bass), they will reduce the standing wave issues that exaggerate the resonances.

There is no way to electronically address resonances with a single speaker or set of speakers reproducing the same signal. The only real electronic remedy is to vastly reduce the frequencies which cause resonances using a notch EQ filter, or multiple notch EQ filters, tuned to the exact frequencies which are resonating in the room. While that remedy can reduce the audibility of the standing wave resonances, it cannot eliminate impact resonances where a "thud" in a recording causes all the resonances in the room to ring. Likewise, an EQ solution cannot compensate for changes in speed of sound which occur with the temperate, barometric pressure, and humidity change. So, one could be forced to recalibrate an EQ tuning solutions several times a year (or several times a day depending on their home environment) in order to get the benefits of an electronic remedy.

Likewise, if the electronic remedy is used, the solution is to cut any energy at the problem frequencies. There could be a dozen problem frequencies for any given listening location, and they will very from location to location. If you are forced to cut two dozen frequencies in order to smooth out the room resonance caused peaks and nulls in the frequency response, then what is left to listen to? I'd rather not have a bunch of the audio signal removed in order to improve resonance issues.
Good stuff, Flint. Good stuff indeed. Keep it coming!
While I am merely scratching the surface, I would hoping this would spur some questions and dialog on the subject. I'd rather not write a 500 page book in the forum which nobody reads.
That's good enough for me, Flint. I'm moving all my gear outside, close to a current bush, of course. No walls or obstructions of any kind, only flat surface will the ground, and maybe the ocassional interruption from a plain flying overhead.

Flint said:
While I am merely scratching the surface, I would hoping this would spur some questions and dialog on the subject. I'd rather not write a 500 page book in the forum which nobody reads.

Patience, there will be questions, and I assure you, your posts are being read by many.

Good weather Saturdays are notoriously slow, and as I told Zing in the beginning, build it and they will come.

So I guess what your getting at is that a good solution is to determine the root frequency of any modes in the room and install a bass trap that absorbs the energy at frequency. Right? Measuring frequency response sweeps with some sort of RTA should be easy enough. The trick then is to know how to build/place a trap that will work at the desired frequency range.

I assume that resonance measurements would require a more sophisticated test rig. I recall looking into RT60 calculators but they were beyond by budget and skill to operate.
Bass traps tuned to specific frequencies are, indeed, good solutions to specific standing wave issues, but they do not address overall bass ringing across the broader spectrum.

There are ways, though difficult, to build wider range bass traps using the panel trap method. I used some pretty crazy modeling (with help from a MIT grad) to design the panels traps in my HT to be centered on the frequencies I calculated to be the resonance frequencies of the room based solely on dimensions. The math for calculating room standing waves is very simple, and Ethan Winer's ModeCalc program is the easiest to use:

By the way, the math to determine the root standing wave for a given dimension is this:

Speed of sound / distance = frequency

Speed of sound = 1128 ft/sec

So, if the distance between two walls is 25 feet, the math is as follows:

1128 / 25 = 42.15Hz

Note that the speed of sound will vary depending on the temperature, altitude, barometric pressure, and humidity. So, the specific frequency being calculated can be treated as +/-5%.
Does the same math apply to arrive at the average frequency considering all three measurements (Width, Length, Height divided by 3) of the room? Also, if those surfaces are treated, doesn't that change everything?

Rope said:
Does the same math apply to arrive at the average frequency considering all three measurements (Width, Length, Height divided by 3) of the room? Also, if those surfaces are treated, doesn't that change everything?


No, you cannot average anything. Each dimension has its own set of resonant standing waves.

No (typically), absorbers like foam, 2" of OC703, or heavy drapes will not impact bass below 150Hz. Only true bass traps can absorb bass enough to impact the low end standing waves.
I've had modecalc on my computer for some time. After using it a few minutes ago, I remember why I don't use it. My room sucks and it's very depressing to look at the results.

Yeah, I have a crappy room for acoustics in this sense, since all the dimensions are multiples or have common factors - 8x12x16.
My space is 27 x 28 x 8 not ideal – on the second acoustics go around built 34" wide Superchunks on all 4 corners - all absorbers (16) are 4” / 6” thick 3 in ceiling – plus the 12 diffusers behind the speakers – must say the 2 channel Maggie’s never sounded better especially after placement tweaks last week – HT section has never been a problem.
i noticed at lowes today the have dow saftey touch insulation and green fiber insulation,can either of these be used for panels or traps?-
PaulyT said:
Yeah, I have a crappy room for acoustics in this sense, since all the dimensions are multiples or have common factors - 8x12x16.
Ouch times 2 times 4 times 8! :scared-yipes:
nats said:
i noticed at lowes today the have dow saftey touch insulation and green fiber insulation,can either of these be used for panels or traps?-

I do not know anything about either of those products.

In my home I use soft batting insulation for bass traps in my small live recording room. I basically have a 18" x 18" strip of soft foberglass insulation running the length of the wall/ceiling corner then running from the ceiling to the floor in each corner, kinda making an alcove at one end of the room. The bass performance was massively improved using that design.

Here's a photo:


I also built dual tuned mid-bass trap treatments for the side walls:

To reduce loose fiberglass from floating around the room I used fiberglass bat insulation which was inside a gray tube of thin plastic. It works very nicely to contain everything. If this were a HT or living space I would cover the fiberglass with wood frames having fabric stretched over the open areas. I already designed those frames for this room, but I'd rather spend my money on microphones or drum head and my time on making music.
Do the soundwaves penetrate the plastic to be absorbed by the batting or is it merely to disrupt or eliminate a corner?