### My Home Studio - Construction and Design

### Making Plans

Having learned just enough to be dangerous, I started scoping out some basic plans. Part of the plan is to adjust as I go along, since I will need to tune the room somewhat interactively. Here's the basic floor plan I inherited from our earlier efforts with the band room (this layout is drawn in Cara CAD):

Based on what I've learned so far, my initial plan is to go with a wood floor, fiberglass insulation (Owen-Corning 703 and/or 705) in the ceiling, and a combination of reflection, diffusion, and absorption, including bass traps on the walls. There's little I can do about the noise of the furnace and hot water heater, except record when they're off. However, I can improve the aesthetics by boxing in the furnace area. The garage door opener and door support are problematic. We had left those hanging into the room when we built the practice room, and they are still supporting the garage door. I was tempted to remove these, but my wife nixed that idea - too destructive. So I need to find a way to hide them.

The location of the mixing console is also an issue to be decided. Ideally, the mixing location should be one one of the shorter walls. However, the room around the mixing position should be a symmetrical as possible, and there is little symmetry (acoustically speaking) in this room. The west wall will have the boxed in furnace on one side, and have an 8.5 ft ceiling to the left and a 10 foot to the right. The east wall has a door on it, which may make a symmetrical setup difficult. and also the garage door opener. In addition, I'd like to be as far from the furnace as possible when recording, because the mics can even pick up the pilot in the gas water heater. I'm considering using the southwest corner ((upper right corner in the diagram), leaving the east side of the room, (to the left, furthest from the furnace), as a recording area. We'll see.

### Reverb Times and Absorption Computations

To start, I can compute some basic information about the room, reverberation times, and how much absrobing material I may need. The room is 14.5 by 12.9 ft, with a 10 ft ceiling, ignoring the irregular shape caused by the door and furnace area. This means I have 922 square feet of surface area and 1870 cubic feet of volume.

The reverberation time, RT60, of a room is given by the equation
*RT60 = 0.049 * Volume/Absorption*, where absorption is computed
by adding the surface area times the absorption coefficient of each
surface and object in the room. Absoption is measured in units called
Sabines. Absorption coefficients are frequency dependent (and
can be looked up online and in books). If I calculate this for my bare
room, using wood floors and drywall walls and ceiling, I get a graph
of reverberation times like this:

I can turn the Sabine formula around to see how much absorption I
need at each frequency to get the reverberation time under
control. The equation becomes *Absorption = 0.049 *
Volume/RT60*. So if I want an RT60 of 0.5 seconds, I need 0.049 *
1870/0.5 = 183 sabines. According to my drywall figures, I already
have 220 Sabines at 125 hz, but only 40 Sabines at 1KHz. Owens
Corning 703 fiberglass panels have an absorption coefficient of 0.9 at
1Khz, so I'd need to add (183-40)/0.9 = 158 square feet of this
fiberglass, distributed around the room. This is only at 1Khz, I need
to work out how much absorption I need at all frequencies and balance
different materials to get a reasonable RT60 time across the range.

Room Modes

There are several calculators available on the web that compute room modes, resonant frequencies caused by the room size and shape. The simple calculator below graphically shows my room modes. Based on my room dimensions, I have primary modes at 38.97 Hz, 43.8 Hz, and 56.5 Hz. I then have modes at all multiples of those frequencies. Since these frequencies will get a boost from the room, they contribute to the "color" of the room. One needs to be particularly concerned with any modes that are reinforced along multiple axis, which this calculator shows graphically along the bottom.

**Axial room modes for my room**

From the colored lines along the bottom, we can see that there are buildups of multiple modes in several places. There are 2 modes right above 300 Hz, which correspond to a mode at 311.72 along the length of the room, and 306.59 Hz along the width. There are 3 modes just below 400 Hz, which would be the 389.66 along the length, 394.19 along the width, and 395.5 for the height

There's a more complex calculator available from the Yahoo acoustics group that computes tangential modes as well. Here's the screen from this calculator for my room:

## Modeling the Room

I used Cara to do some initial room modeling. I'm somewhat skeptical about the accuracy of these calculations, since the input data may not be entirely accurate, but it was educational. Cara allows you to plot and graph many different pieces of information. Here are a few.

Starting with the bare room, concrete floor, drywall walls and ceiling, Cara says my reverberation times are as follows:

**Reverberation times of bare room, with no treatment**

The green lines are the upper and lower bounds of what Car considers to be ideal. The red is the calculated Sabine RT60 times for my room. As one would suspect, the reverberations times in the bare room are much too high. Cara seems to think my gypsum drywall ceiling and walls will absorb a lot of low frequencies, which matches the sabine calculations above. The curve of the reverberation times is not exactly the same as my calculation, but the general idea is the same.

Another interesting graph Cara can produce is a "Coloration" graph that shows how much the room colors the sound at different locations. For this calculation I assumed my mixing position in the upper right corner of the diagram. In this plot, blue is good, little coloration, red is bad, a lot of coloration:

**Room Coloration of bare room with no treatment**

There seems to be a fair amount of coloration in the middle of the room.

Cara also computed the frequency response of my speakers in the room as heard from the mixing position. The green line is the desired response (according to Cara) while the red is the result of the speakers in my room.

**Speaker frequency response in the bare untreated
room**

Just for curiosity, I specified acoustic foam for all walls and ceiling, and reran the calculations. Again, as expected, the foam has dramatically reduced the reverberation time (too much), but only at higher frequencies. Cara now seems to believe my walls will no longer absorb the lows, and I have an 800 ms reverberation time below 150 Hz.

**Reverberation times in the room covered entirely in foam**

Looking at the coloration graph for the foam-covered room, we see that the room is fairly uncolored, except right in the corner where the speakers are positioned. I guess completely dead, at least at high frequencies, eliminates coloration, even though it may not be a very pleasant room to be in.

**Coloration in the room covered entirely in foam**

Finally, I tried to model a more realistic room treatment. I added, in Cara, about 50% ceiling coverage of acoustic foam, a couple of corner bass traps, and a few more foam panels on various walls, including behind each speaker. I also added the structure that should box in the furnace. Cara now computes the reverberation time as follows:

**Reverberation times in the realistically treated
room**

The red line, representing the room response is now right in the middle of Cara's desired range, tho the times are a bit shorter than my goals. With this partially foam covered room, the coloration is computed to be:

**Coloration in the realistically treated room**

The coloration graph seems to look mostly good. The red areas are inside the boxed in furnace area and inside the corner bass traps. I can imagine that those are not places one would want to be standing to get the best sound!

With a reasonable foam treatment, Cara now calculates the frequency response of my speakers at the mix position to be somewhat flatter:

**Frequency Response in the
realistically treated rom**

These diagrams and calculations are interesting, but I doubt they are very accurate. Cara didn't seem to understand my bass traps, and I didn't take the time to enter correct data for Owens-Corning 703, and just used the built-in "acoustic foam" material Cara already knew about. But Cara seems to be powerful enough that I could develop a more accurate model with enough effort, adding data for bass traps, 703, etc. The shortcomings are more of the garbage-in-garbage-out variety. Still, the process helped my understanding of the room and how I may proceed with treatment.

At this point, I know that I have some room modes to watch for in the 300-400 Hz range, and that I need to reduce the reverberation time by ensuring that I have about 183 Sabines of absorption at all frequencies. I need to do some real measurements and see what I have to start with.