# The Biggest Problem With Mixing In A Small Room

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When I enter the dimensions of my room into this calculator, it calculates the resonant frequencies.

This resonance at 42 Hz is caused by the spacing between the front wall and back wall, as you can see with the blue and red indicators.

Let’s play this tone through a speaker in my room…

These three standing waves are referred to as “axial room modes” because they occur between two surfaces. (front to back wall, left to right wall, and floor to ceiling. This type of room mode is the most extreme, and is therefore one of our main focuses when thinking about the acoustic quality of a room.

Another way to visualize this is to use a string and a transducer…

When the transducer moves the string at its resonant frequencies, we will see points where there is a lot of movement (called antinodes) and points where there is no movement at all, (called nodes).

This demonstration describes what is going on with the acoustics in my room. Kind of…

To understand why this particular string example is flawed, look at these animations by Dr. Dan Russell at Penn State University… [Reference for b-roll: https://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html]

You can see nodes and antinodes, similar to the string demonstration, but this time we’re dealing with a longitudinal wave. Think of these dots as air molecules that are being bunched together (in compression) and spaced apart (in rarefaction), just like sound waves.

Notice that these two red dots are moving a lot – they speed up, slow down, then speed up in the opposite direction. Meanwhile this dot doesn’t move at all.

Below this animation, there are two additional graphs. One shows displacement (the movement of the air molecules). The other shows pressure (the concentration of the air molecules).

The stationary dot isn’t displaced at all, and is therefore aligned with a node on the displacement graph. However, the stationary dot is aligned with an ANTINODE on the pressure graph.

In fact, all of the points of maximum pressure line up with points of minimum displacement and all of the points of maximum displacement line up with points of minimum pressure (at this particular frequency).

We can see this at various other resonant frequencies, too. Maximum displacement, minimum pressure. Minimum displacement, maximum pressure. [Reference for b-roll: https://www.acs.psu.edu/drussell/Demos/StandingWaves/StandingWaves.html]

So why are these animations (and the string example from earlier) flawed visualizations of ROOM modes?

Well, on one end of the graph, we see a fixed boundary, but on the other end, there is not a fixed boundary…

Dr. Russell said it himself right here: “The particular example of a standing wave that I want to illustrate is a standing sound wave in a pipe that is forced (by a moving piston or loudspeaker) at the left end and closed at the right end.”

Listen to the sound of this pipe with a cap on one end versus the same pipe open on both sides…

If you were paying extra close attention, you might have noticed that the nodes and antinodes in these animations don’t really align with the listening example from the beginning of the video.

Remember – you heard an antinode of pressure when you were close to the walls. That’s not what we see in these animations, because in these animations only one end is fixed.

ALL of the boundaries of a ROOM are theoretically fixed, which results in standing waves more similar to those you’d see from a string that is fixed on both sides, like a guitar string.

This makes sense, right? I mean, there won’t be much displacement of anything here at the wall. Think of the air in the room as a big spring. When a sound wave compresses the particles against the wall, there will be a lot of pressure, but very little displacement. Most of the displacement at this frequency will occur toward the center of the room. And on the other wall, there will be another point of max pressure, minimum displacement.

Just like the pipe examples, there will be additional resonances within the room at higher frequencies.

Let me quickly mention that these frequency calculations are theoretical, assuming totally reflective surfaces. The reflective properties of the walls, floor and ceiling will ultimately determine the exact frequencies that will resonate, but in this case, it’s pretty close to reality.

As you keep going up in frequency, you’ll see that the location of the nodes and antinodes will vary, sometimes a node in the center, sometimes an antinode in the center, but there is always maximum pressure at the boundaries.

Here is another room mode calculator by Harman that illustrates where you can expect nodes and antinodes of pressure throughout the room, at its axial mode frequencies.

One of the most cost-effective and popular acoustic treatment options is a porous absorber (sometimes called a velocity absorber) like this Monster Trap from GIK Acoustics. You can find a link to this panel in the description below the video.

These absorption panels come in many shapes and sizes, but the DEPTH of the panel is particularly important. That’s because porous absorbers like this convert acoustic energy to heat through friction – and friction requires velocity.

Think about what you’ve learned in this video so far… Where are the areas of maximum velocity in this animation?

Well, the particles against the boundary have very little velocity – remember, they don’t move much at all. And the particles that move the most will move very quickly, then slow down as pressure builds, and then move very quickly in the opposite direction, until pressure builds again. So the points of greatest velocity are right here in the middle of those paths (particularly, the points of minimum pressure).

If you place a velocity absorber like this one directly on a wall, you’ll be placing it in an area of maximum pressure, not velocity…

That’s one reason why there is an air gap behind these panels in some cases, because a porous absorber directly against the wall will only be effective at higher frequencies that have shorter wavelengths. The thicker the panel, the more effective it will be at lower frequencies.

A helpful guideline is the “¼ wavelength principle”, which tells us that we need a porous absorber with a thickness of at least ¼ the wavelength of the lowest frequency we want it to absorb.

This panel is about 7.5 inches thick, so the ¼ wavelength principle tells us that it can effectively absorb frequencies down to about 450 Hz. Although, you can see here that it is somewhat effective below that frequency.

Meanwhile, this 3.6-inch panel is most effective down to about 1000 Hz.

This means that if we use a ton of thin panels in our room, we will be absorbing mostly higher frequencies, resulting in a build-up of low-mid and low frequencies. Depending on the application, that’s ok. But if you need low-frequency control, you will need thicker panels.

You might ask, can’t we just place velocity traps away from the walls? That’s a good question, and it indicates that you’re thinking about it the right way… But there are a few additional variables, like the horizontal and vertical dimensions of the panel versus the wavelength of sound waves that will simply go around it. Plus, there’s the practicality factor…

I need space to move around for efficiency and creativity more than I need better absorption at low frequencies. And so, I have chosen to use thick panels, placed along the boundaries of my room, with a relatively small air gap behind them.

At a certain point, you’d need panels that are impractically thick to absorb the lowest frequencies. And that’s why there are pressure traps that operate in a way that works best in areas of maximum pressure…

Another reason the relationship between pressure and displacement is important is for selecting the listening position and speaker location.

You might have heard of a guideline referred to as “the 38% rule”. This shouldn’t be taken as a hard fast rule, because (again) the wavelengths that resonate may vary depending on the reflectiveness of the walls and ceilings. But, it’s a helpful starting point.

The 38% rule would suggest that a good starting point for the listening position would be about 38% into the length of your room, as this is where the first few modes in that dimension will be most balanced.

For stereo image, we usually sit directly in the center of the two side walls – so we will be at a complete null for the first two modes. And, with my 8ft ceilings in this room, my listening position ends up at nearly the exact center…

The source location also matters. The room will respond to each resonant frequency most when the source is at a point of maximum pressure. Here’s a helpful animation that illustrates this concept…

The red dot is the position of the speaker on this plane. At the areas of max pressure, the room has the most extreme response to each frequency while the room will theoretically not respond at all if the speaker is in one of the pressure nodes.

If we place our ears in a position where there is a pressure antinode and then move the speaker to a pressure node, we will hear that there is a dip in the room’s response, but we still hear this frequency somewhat because this is a 3-dimensional room, not a 2-dimensional theoretical animation.

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