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# What are room modes?

To explain room modes from the very beginning we have to start earlier.

## What are resonances?

The easiest way to explain a resonance is by giving an example. Let's say you push a child on a swing...

Think about you move the child veeeery slow up to a high position and then you walk back slowly again and move it on the other side up to a very high position and so on.

Imagine moving the child veeeery slowly up to a high position, then slowly walking back and moving it up to a very high position on the other side, and so on.

I'm not sure if the child will have fun, but you will for sure have a very hard time to do so depending on what you feed your child.

Now think about the other extreme. You move the child very fast forward and backward, much faster than it would normally move on that swing.

Easy to imagine that this also would need a lot of energy on your side.

Both extrems need a lot of energy but you know from experience that somehere in between it's pretty easy to let the kid swing very high without constantly inducing energy into the swinging system. In fact there is exactly one frquency where it is easiest and that's the resonance frequency of that whole swinging system.

Excursus: spring/mass system

Every spring/mass system has such a resonance frequency where movement finds the least resistence. And every such system will move at this resonance frequency when you push the mass (squeez or stretch the spring) and leave it alone. The spring will try to move back to its original position and the mass will (because of the inertia of its mass) let the system move over this position some times before it finally stands still again. Depending on the friction (dampening) it will move longer or shorter.

But where the hell is a spring in a swing? Also if there is no spiral built in most swings, we can still find the equivalent of a spring in the dance between 'kinetic' and 'potential' energy when a pendulum (like our swing) moves. We have potential energy stored in the system when the kid is far up in the air because the kids weight will eventually fall down because of earths gravity as soon as we don't hold it anymore. It builds up speed and right when it passes the deepest point on its way to the other side it will have its maximum kinetic energy. As it can not fall deeper (at least not while still sitting in the swing) there is no potential energy anymore but you could feel the amount of kinetic energy when you would try to stop that kid aprubtly by stepping into its way. It would feel pretty much similar to what you would feel if the kid would have fallen down form its highest position directly onto you lying on the floor. Yes, this is quite some energy.

Ok, with all that energy in that system, how can you induce all that energy necessary to let your kid move high without even getting your heart rate up? That is because of two things. Firstly, as I wrote above, the system looses very little energy because of the low resitence and secondly because of your timing. It's enough to give the kid a short push at the right time. This builds up as there is still energy from your last push in that system.

With all that in mind, let's go back to our context of room acoustics.

Think of the membran of your loudspeaker as the guy pushing the swing.

It's not a single air molecule but the whole mass of the air in our room that acts as a wobbling mass.

The fact that the air will always try to be homogenously distributed in your room acts as spring.

This is how the air in your room will not act.

This is how it will act.

So when you push the air in one direction it will flow back. Doing so, it will act like the simpler swing acts. It will first move over its point of rest because of its mass inertia. And like the swing will eventually end it's oscillating movement, the air will as well. And this will need time depending on the amount of dampening (here we call it absorption).

## Resonances of 3 dimensional wobbling air (= room modes)

Because we have three dimensions now and maybe a very complex shape of the rooms volume (not just walls, also furniture) it's not that easy to calculate the exact behavior of that moving amount of air. Also walls are not really that hard especially at low frequencies.

It can be done with the help of the so called FEM (finite element method) but it needs time to get a model of the room that is exact enough and even with a modern computer it needs time to calculate it.

Here are some examples for room modes in non shoe-box shaped rooms.

Room mode estimation of such rooms is easy now with amroc pro, the new room mode calculator for non-rectangular rooms. It's using the Finite Element Method under the hood.

Excursus: Finite Element Method (FEM)

You basically have a virtual model of the room and fill it with virtual air. Then you calculate how those atoms (they call it 'finite elements') interact acoustically. Fortunately, you don't need to calculate every single atom in your room, but you need at least some per wavelength.

The easiest way to use the power of the FEM is by using my amroc pro room mode calculator for non-rectangular rooms.

There are also other methods like the Boundary Element Method (BEM). If you are more interested in all of that, ask your favorite search engine about 'Numerical Acoustics'.

Fortunately a lot of our rooms have a shape where a mathematical simplification for calculating the room modes exist. For rectangular rooms we can calculate the modes immediately. And that's what amroc is doing. Where amroc pro needs powerful servers to do the FEM, the simplification for rectangular rooms can be calculated in your browser, even your mobile phone as long as you don't type in very "unnatural" values.

The simplest room mode is the so called 'axial' room mode.

Let's have a deeper look at it and compare it with our well known swing from before.

The sound moves away from the speaker when the membrane changes the local air pressure. At low frequencies a speaker normally radiats sound in all directions. So the wave is reflected on the nearest wall first.

For simplicity reasons we will only watch one part of the wave as it moves on in the room and exclude reflections of other parts of the wave from our observation.

The wave is reflected at the back wall.

It comes back, is reflected again from the front wall (behind the speaker) and right when it passes the speaker again, the membrane pushes it again and the whole cycle repeats.

2 walls are involved in such an axial mode. The following images show, why it can be important to understand which walls are involved in a particular room mode.

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## Axial, Tangential, Oblique Modes

The next images are 3D visualizations in my room mode calculator amroc for the calculated modes. The blue and red zones both show pressure zones of the modes. Amroc shows those different colors just for better visualization for higher order modes.

Because the modes are narrow band and acting locally it is important to understand at which places a subwoofer or absorber should or should not be placed (more about that later).

## What are those number patterns for each mode?

In the pictures above and in my calculator you can see patterns like '1-0-0', '1-1-0', '3-2-4',... Let me explain what that means.

The deepest mode that can occure is when half of a waves length fits between two walls. The next mode happens at twice that frequency, the next at three times that frequency and so on. 1 stands for that first (half wave length mode), 2 for the second and so on.

A sine wave (wave with one particular frequency) looks like this.

This is a full wave length, so it is already the index 2. Index 1 stands for a half wave length looking like this.

That's the sine waves we are visually familiar with. But it's a little bit misleading when we speak about room modes. When we say the left and right borders of the graph are the walls of our room then this line would show us the particle velocity in such a wave (no movement at the borders).

It makes sense to plot the pressure because that is the thing we hear. Now it looks kind of like the opposit. We have max pressure at the walls looking like this for index 1

and like this for index 2 of our axial mode.

When particles move close together (high pressure), they can not move freely anymore (low velocity). You also see that velocity has a direction (first plot has a negative and positiv site), the pressure plot goes just from 0 to max pressure.

When you look at those 3D pictures again I hope you see the similarity to my simple pressure plots.

So for axial modes it's pretty easy. But also for the others it's not that hard. Let's take this example of a tangential mode again:

If you would walk along the length of the room you would walk through 3 pressure zones (2 dips) again, like in the above pictures on the right. It's therefore index 2 for the length. On the width we only have pressure zones on the walls like in the left pictures above. For the height there are no peaks and dips, it's zero. The index pattern is 2-1-0.

Last but not least one of the above examples of an oblique mode again:

3 pressure zones on the length, 2 for width and height. Index 2-1-1. Either subtract 1 from the number of pressure zones, count the dips, think about the number of half wave lengths or just don't think about at all. It's just a way of giving each mode of rectangular rooms a name.

# What is the problem with room modes, why are they so bad?

Normally we want our room to sound neutral in a way it does not change the music we are listeneing to. We don't want every C played by the bassist of our favorite band be very loud and long and every E played by the same guy to be non existend. We want them to be exactly as lound in relation to each other as the bassist wanted them to be. With strong modes in our room it is absolutely possible that something like the above can happen. And its even worse. While at our position each C may be much louder than each E, at another position in the room it may be the exact opposit. So we can not even use a equalizer to turn down the C and amplify the E. We really have to add friction/absorption/dampening into the swinging system.

The next picture shows a relatively quiet room analyzed with my amalyzer tool. This tool simply records audio coming from your standard microphone. It shows a spectrum on top of a piano keyboard. In addition there is a spectrogram underneeth that shows energy over time (the area with the black background). We can clearly see that there is a narrow band phenomenon amplifying noise around one frequency (vertical green/purple line from top to bottom of the spectrogram). This phenomenon is a room mode and you can easily spot that the room will add 'sound' to every music at that frequency.

As I wrote before we have to add friction/absorption/dampening into the swinging system at such frequencies to minimize this 'sound-effect'. Either narrow band absorption with resonance absorbers tuned to the particular frequencies of our modes or by adding broad band absorption in the whole low frequency range. It needs a lot of space, costs money and/or time and we would prefer to spend that money on our audio system. But fact is, at low frequencies the room will harm the record much much!! more, than your player, cables or amplifier will. So please, if you want to spend a lot of money on those and much less money on your room, ask yourself what your goals are and why exactly you spend what amount of money on which part of your reproduction chain.

I would like to add comparisons of transfer functions of bad, normal, best cables, players, amplifiers and speakers here and compare them with transfer functions of bad, normal and best rooms. If you have such transfer functions to contribute, please tell me.

# Conquer room modes

Unfortunately there is not the one easy solution for letting room modes disappear. But now that you have a deeper understanding about what they are, it should also be easier to decide which direction you are willing to go.

## Foam

I start with foam, because foam and other porous material (carpet, curtains,...) are the most common and best known acoustic tools in the world. Unfortunately maybe they are also the most misunderstood tools. Not because it is too complicated to understand how it works, but because it's so easy to understand. Everyone can imagine that moving air molecules have a hard time swinging inside of such materials. So people take this image and sell foam in all colors and shapes all over the world. Each of those products is finally the best you can get for your money.

With my described huge amounts of air still wobbling around in your head I guess you do understand now why thin foam is not a solution for the problem. Let's say the amount of wobbling air mass involved is just overwhelming for a little bit of foam. But I'm too pragmatic to say it's not possible. You just need a lot of foam. And for a lot of foam you need alot of space. So if space and foam is easier and/or cheaper for you to get it maybe can be one solution for you.

Try to get a porous material with a very low flow resistance and stack it deep. I mean really deep. Read my in-depth explanation on porouse absorbers and how their depth and properties relate to their acoustical efficiency here. Place them in the corners of your room to further increase their effect.

## Room Dimensions

This is one of the strengths of my room mode calculators amroc and amroc-pro. If you are in the lucky position to build a room as a whole you should try to set the length, depth and height of your room in a way, that the modes are well distributed. That means, you should prevent multiple modes falling together in one small frequency range.

Think of it like that: you simply have a huge amount of room modes. They are there, no matter what you do, no matter the room shape and size. What changes is their distribution in the frequency spectrum. So try to distribute them in a way where they make the least amount of problems.

The modes in bigger rooms start at lower frequencies, in smaller rooms the modes are higher up. That's why bigger rooms have less problems with modes, as the range where modes are problematic is at deeper frequencies, where our ears are less...let's say accurate.

Deep down at the lowest mode frequencies there are just a few of them as you can see with amroc.

With increasing frequency, also the mode density is rising. You also see piano keys in the background of the picture. Their job is to visualize musical notes as those are well suited to show if the modes are dense enough or if a gap between a bunch of modes is too big. Still remember the bass player I wrote about above? If he plays a note in one of those 'mode gaps', the note would be kind of 'normally loud'. But if he would play a note backed by a mode, it would be louder or maybe it would not be audible at all depending on where you are in the room. If there are enough modes at the played frequency it kind of smoothes out. Above the Schröder Frequency the note should be backed by some modes no matter where you are in the room.

So our problems happen down at that frquency range where room modes exist but not enough of them. They are not close enough together yet to smooth out. What we can do is we can build a room with dimensions that let the modes be as eqally distributed as possible. That's also what Oscar Bonello had in mind when he invented the Bonello Criteria. It is a fast and easy way to see if room dimensions make sense from a modal point of view. He stated that the number of modes per third (a third of an ocatve consists of 4 notes) should always (strictly) increase to higher thirds. You can see this function increasing in amroc as well.

Increasing number of modes per third
Not always increasing (cube room)

So, what you don't want, are accumulations of modes and gaps between those accumulations. Because the room would respond different in those two frequency ranges. Modes will always become denser to higher frequencies. The smoother they grow in numbers the better. The Bonello Criterum tries to make this smoothness visible.

A great video about finding the right room dimensions is "Why Room Ratios Don't Work...Most of the time" from Wilson Harwood.

To clarify the title: it's not against thinking about the right room ratios, it's a plea for not simply using 'ready made room ratio presets' but using modern tools to find the right ratios for your specific use case.

Also if I think room ratios like those from Sepmeyer, Bolt, Louden, etc are not relevant anymore, I should add some information about them here. They are hostorically relevant...tbd, like many other things.

Oscar Bonello was not the only scientist who worked in the field of room modes. Richard Henry Bolt is known for his Bolt-Area which you find in amroc as well.

The Bolt-Area diagram for a room 500 x 400 x 300cm.
That's the same ratio as 1.67 x 1.33 x 1 (all room dimensions divided by the room height / 300cm).

The Bolt-Area was a way to find good room ratios when computers were not widely available. R.H. Bolt created this diagram to indicate an accumulation of good room ratios. Two dimensions of the room (let's say width and length) are plotted on the two axes of this 2-dimensional diagram. The third dimension (height) is constant. This is possible because the room mode distribution does not change with the size. They all just move up when the room gets smaller. The axes could go from 0 to infinity, showing the ratio between that dimension on that axis (width/length) to the height. So a value of 1.2 on the length axis means, that the room is 1.2 times longer than it is high.

With this structure, you can now calculate the room mode distributions for all possible dimension ratios and color the pixel at that position in one color for good mode distributions and another for bad ones. Once he did this he discovered an area on this canvas where lots of good room ratios accumulate. He drew a line around this accumulation and released the so-created Bolt-Area to the world.

Back in the 1930ies, when R.H. Bolt did this, there was no easy way to calculate and visualize room modes. So people could simply use this newly invented diagram to see if a specific room ratio is inside that Bolt-Area, increasing the chance of being near a good distribution.

I added this diagram here and in my room mode calculator as it has excellent historical relevance, but I recommend not taking that shortcut today. Instead, you can enjoy the possibilities of the computer age and analyze your possible room ratios with great visualizations in no time. Sure, it can be overwhelming at the beginning to dive deep, but hey...this article should be of great help here :).

Also, as the Bolt-Area is a simplification for rectangular rooms, it never helped with any other room shape. In amroc pro, the room mode calculator for non-rectangular rooms, the Bolt-Area would therefore be of no help.

## Resonance Absorbers

The previously mentiond porouse absorbers are light and don't interact much with the incident soundfield. In the group of resonance absorbers we now have some heavier mass that can only be moved by incoming sound because it is mounted in a way where it is itself a mass/spring system and can therfore be excited by the impacting mass of the sound wave. It is interesting to know that such absorbers not only change the level of sound but can also change the structure of the sound field as they are a kind of sound source by itself.

A lot of materials can be used as resonance absorbers: plasterboard, glass, timber and also dense foils and leather have been used.

Now that you are an expert in resonant mass/spring systems I can keep it short. The plate or foil in front is the mass. The air behind acts as spring. OK, in fact we also have a mounting and a flexural behaviour of the plate that contribute to the spring as well and that makes the resonance absorbers a little bit more tricky than their porous siblings.

Read more about optimal construction and why they only act narrowly or with little absorption here.

If you have built such absorbers or know about some construction manuals, let me know and we carry them together.

## Active Absorbers

Instead of removing energy from swinging air by using that energy to move some tuned mass, active absorbers somehow measure the pressure infront of itself and try to suck up that pressure to absorb it.

Here are two examples. If you know of anything else. Tell me and I will add it here.

## Placement of Absorbers, Sound Sources and Listener Position

The Theory is as follows. For frequencies that are deeper than the deepest mode, in between gaps of modes and where modes are very dense the position of sound sources and listener should not be so important. If you only have one or a few modes around that frequency those positions make a difference.

One usage of my room mode calculator is visulazing where the pressure zones of a specific mode are. So when you have a particular frequency that bothers you, either because it is too strong or it is too weak, you can get help by searching this frequency with amroc or amroc pro. Once you have found it you get help by the 3D Visualization. This visualization shows you the pressure zones of each nearby modes, making it easier to identify the one you have problems with.

Once you have identified that mode you can move your listening and/or source positions either in or out of the preasure zones.

Subwoofer: The more your speaker is inside of a pressure zone, the more you excite the mode. Is the subwoofer outside of the pressure zones you can not excite it and maybe hear nothing. So depending on what you want to achieve you can move the sub in (if you have a dip in your frequency chart at that frequency) or out (if you have a peak).

Listener: It's pretty similar to the subwoofer position. You ear is a pressure transducer and will hear the most in the pressure zones and down to nothing in between.

Absorber: The best and therefore the usual place for your absorbers is in the corners of your room. In addition to that you can place resonance absorbers in the pressure zones of your modes (max pressure) and porose absorbers in between (max verlocity).

## Double Bass Array

I wrote about that complex wobbling of the air mass above. Another way of tackling room modes is to excite the air so that it wobbles less complexly. Sounds a bit like a fantasy of a science fiction author but in fact it's relatively easy.

Let me split up the name 'Double Bass Array' to explain what it does. 'Bass' is easy. It just means that we use it for deep frequencies.

The 'Array' part of it is what matters most. Normally when a speaker plays a low frequency sound, a spherical wave front radiates into the room. In a DBA we use multiple sub woofers to excite a plane wave front instead. It's like you have a pipe and some piston that fits in it. Or even better, imagine we move one wall of our room as a whole. We would push the air everywhere at that wall at the same time. Therefor the air can only go in one direction - away from that wall. There will be no movement to the side, just straight away from the wall like in a tunnel. The cool thing about that is, without the air moving into the sidewalls, we also have no reflections from the sidewalls. And therefor we can only excite the axial modes between the moving wall and the wall on the opposite end of the room (please tell me if this implication is not well enough explained).

So the only modal stuff we have to conquer when we use such an array are those axial modes. And that's where the 'Double' comes into play. It's quite easy to absorb such a flat wave front with the exact same loudspeaker array on the other end of the room. Remember that swing at the beginning of this article? How do you stop it? Exactly, when the kid is on your side you try to catch it, absorbing the kinetic and potential energy in the system. The same happens when some speaker cones move away from the wave front the moment the wave front arrives. Normally the wavefront would hit the wall, building up pressure and because of the fact that air wants to be homogenously distributed it would move back to release that pressure at the wall. But as the membrans of the second speaker array move away at that very moment the pressure can not be build up and the wave is not reflected. It's kind of sucked up by the speakers.