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Shape Into Sound
Designing a project studio from the bottom up...
By Amy E. Bieber

What does your room do to your sound? Does it matter? You bet it does! This article shows how to design a project studio for your house in such a way that recordings you make there will sound good no matter where else you play them—from your buddy’s car to the office of a record label’s A&R person

You might have made the best mix of your life in your project studio, but if that room wasn’t designed right, that same mix might sound like mud in the producer’s office—and onto the scrap heap it goes. Here’s how to make sure your recordings sound good no matter where you take them.

Get prices

When you begin to design your studio, first decide how much space you can dedicate to the project. Part of a basement, a full basement, part of a garage, or a full bedroom? This matters, because the dimensions (length, width, height) are among the first things you need to know to design the room correctly. Also, the bigger the room, the bigger the budget, so you need to decide exactly how much money you can commit to this project.

After you have done these two things, visit home improvement stores and look at:

• ceiling tiles—get prices, absorption coefficient of the tile, and frequency information (ceiling tiles can vary widely, so it is important to get those numbers);

• carpet—get prices (most carpet places don’t give you absorption information, but I will give you a reference that has general numbers you can use);

• wall materials—get prices of different types if you’re building the room from scratch.

Here’s where square-footage and calculator come in. For starters, without doing any acoustic calculations, pick the carpet you like and the ceiling tile you like and figure out the cost based on the square footage and price. See how much of your budget is left.

Next, get estimates from an electrician for the electrical modifications (outlets, possible added switches to your box, possible power upgrades, lighting), and from a plumber for a heating system, if there isn’t one. Now, I’d say just add $150 to the total for the little things you forgot that add up later, like switch plates, door knobs, tips, etc.

Now, excluding any audio toys you might want to buy, take the total so far that includes ceiling, carpet, electrical, plumbing and extras, subtract it from your budget, divide what’s left by the total area of your walls, and you will see how much money you have left for wall material. Since you’ve been to the home improvement store and priced things out, you will know if you will have sheetrock walls with metal studs, wood studs, or if you can go for something nicer, like a cedar wood wall.

Goals and budgets

Finally, what is your goal in building this room? Do you want a place just to fool around and make some noise, maybe occasionally turn on a 4-track recorder to immortalize your ideas without the neighbors always yelling at you? Do you want a decent project studio where you can make demos, have your friends make demos, high-quality enough to send to record companies and not get them immediately incinerated? Or are you looking to rent this space out as a professional recording studio within your house?

The price differences between these three scenarios are astronomical and your budget will pretty much determine your option for you. Without having dimensions to work with it’s hard to throw numbers at you, so, using my studio as an example, I can tell you that it cost approximately $12,000 to create a very nice-looking project studio that is 2300 cubic feet in size with lead-in hallway (you’ll get the individual dimensions later).

One note: my studio is in a basement and is reasonably sound-reduced, but not soundproof. To truly soundproof a room is worth an entire article in itself, if not a whole book (and many have been written!), and involves a lot more complexity and expense. We’re aiming here at a room that sounds good inside, not that completely stops sound from outside.

Now that you have a basic idea of the materials to be used in your studio, it’s time to find out if you made good choices. You need to do two things: calculate the natural room resonances based on the dimensions you chose, and calculate the reverberation time of the room you are building and see if it fits with the type of music that will most often be played in that room.

Calculating resonances

Every enclosed object has natural resonances (emphasized frequencies) in it, from a water bottle where you blow over the opening, to the room you are sitting in. In the simplest case, the resonances are determined by the speed of sound and the size, in one dimension (length, width, height), of the room.

First, we need to check the first few harmonics in each dimension of the room to make sure they don’t overlap or come close, to avoid an uneven room sound in terms of frequency; if some frequencies were to be overemphasized, this wouldn’t sound right to your ear and definitely will lead to a poor recording.

Let’s start with the room resonances in each direction. The equation to figure out the fundamental frequency in any direction in the room is:

F = V/2X

Where F = frequency in Hz, V = the velocity of sound (about 1131 feet per second at room temperature and at sea level), and X is the dimension, either length, width, or height (in feet—you can do this in metric if you wish, using V = 345 meters/sec).

Let’s calculate the first 3 frequencies for the length of my room:

The length of my room is 27 feet. Our first lengthwise resonance F1L will be:

F1L = (1131 ft/sec) / (2 x 27 ft)

Here’s how we do it, in two steps:

2 x 27 = 54 ft

1131 / 54 = 20.95, rounded to 21 Hz.

Based on this result we know the frequencies of the first 3 harmonics for the length of my room:

F1L = 21 Hz

F2L = 2 x F1L = 42 Hz

F3L = 3 x F1L = 63 Hz

So, the long dimension of my room supports a lot of bass—I like that!

The width of my room is 11.75 ft., so we again apply the formula:

F1W = (1131 ft/sec) / (23.5 ft)

This gives us F1W of roughly 48 Hz, F2W = 96 Hz, and F3W = 144 Hz.

Now, comparing those numbers to our length resonances, we see F1W is 6 Hz away from F2L. Is that too close? In practice, no—if you can avoid resonances being closer than roughly 5 Hz to one another, you should be okay. (I could have built my room 9" wider, but that would have created too close a coincidence.)

The height of my room (7'3" drop ceiling) gives me

F1H = (1131 ft/sec) / (14.5 ft) = 78 Hz, F2H = 156 Hz, F3H = 234 Hz.

None of these come close to any of the other first three harmonics.

When designing my room, I wrote a computer program to calculate the first six harmonics in each direction, and the only compromise I had to make was in reducing the width a little. I think it was worth it, because the room sounds great. If you end up with any of the harmonics in any dimension within 5 Hz of another, tweak the dimensions a little, even if it means you lose a little bit of space. Think of it as extra soundproofing, if it is against an outside wall, as mine was—there’s no better soundproofing than air space between walls.

Now, this calculation doesn’t cover all of the ways in which sound can bounce around; resonances between opposing surfaces as we’ve calculated here, also called axial modes, are only the simplest of three resonance types—but they have the most effect on sound, and these simple length/width/height calculations will take you far.

If you want to calculate the more complex modes for your room to see if they’re causing problems, there exist Excel spreadsheets and other programs to do this math for you. Check out www.wsdg.com, the site of the Walters-Storyk Design Group. That site’s Resources > Technology page has many acoustic calculators, not only “Roomode” (the one we’ve discussed) but also one for our next topic: reverb time.

Calculating reverb and absorption

Reverberation time (RT60) is the amount of time it takes a sound, once it stops being generated at the source, to decay by 60 dB. In real terms, it’s a measure of how “live” or “dead” a room sounds. Longer reverb times mean more live-ness.

If you have access to a good library, look for one of the many books that further explain reverberation. I like Berg & Stork’s The Physics of Sound (3rd edition, Pearson/Prentice Hall 2005), it has a chart (fig. 8.4 on page 218) that shows the different reverb times that are ideal for different types of music in rooms of different sizes. I chose “recording studio” and looked up the total of 2300 cubic feet, which told me that I should be shooting for a reverb time of a half a second. (The Berg & Stork book also has the reverberation times of many popular materials on page 227 in Table 8-3, and there is even a table for occupied and unoccupied seating in Table 8-4.) It was reassuring when a second book, using a second method, gave me roughly the same result!

The formula for reverb time is simple but tedious, and you only have to do it a few times (once for each frequency you wish to check). It goes like this:

T = 0.050 x V/A

Where T is the reverb time in seconds, 0.050 is a constant that you don’t need to concern yourself with, V is the total volume of the room in cubic feet (which you already know: it’s length x width x height)...and A is the total absorption of the room, which is the tedious part. You have to calculate the surface area of every surface in the room and multiply by the absorption coefficient of the material that is going to cover that surface. These coefficients are what change with frequency.

To make things simple, we are going to calculate this for an empty room. We are not going to include your instruments, your rack, and your friends, so this will make it easier—and not precisely accurate, but close.

Okay, let’s use my room again. I have cedar on the walls, but I will give you the absorption coefficient of generic wood. We’ll do a calculation at 250 Hz and at 2000 Hz to see the difference. I have carpeted floor, an acoustic tile ceiling, plus one wall which is partial glass and partial corkboard (I had to substitute “curtains” below because the chart did not have cork).

The absorption coefficients are as follows—a value of 0 would mean perfect reflection and 1 would mean perfect absorption, neither of which is possible in real life: at 250 Hz (our first calculated frequency) we have 0.20 for the carpeted floor, 0.45 for the ceiling tile, 0.25 for wood, 0.08 for glass, and 0.12 for cork. These numbers will all be different at 2000 Hz, which is why a table of these values is so handy.

About bass: As you move away from a garage where there’s a band playing, the bass will fade last. That is because bass is hard to absorb, but also because of a wave property called diffraction, which allows longer waves to travel farther—but that’s beyond the scope of this article.

Okay, now we calculate the surface area, in square feet, of each surface made of the same material in the room. Then, we multiply the area of each surface by the absorption coefficient of the material covering that surface, to get the total absorption of the surface for this particular room and frequency. All of the absorptions from each different surface in the room, added together, give you the quantity A in our reverb-time equation. The unit of measurement for absorption is the Sabin, named after a famous acoustics scientist.

Floor area (f):

Af = length x width = 27.0 ft x 11.75 ft = 317 sq. ft.

Absorption of floor at 250 Hz = (0.20) x (317 sq. ft.) = 63 Sabins

Ceiling area (c):

Ac = same as Af = 317 sq. ft.

Absorption of ceiling at 250 Hz = (0.45) x (317 sq. ft.) = 143 Sabins

Walls:

Short wall area = 11.75 ft x 7.25 ft = 85.2 sq. ft.

Long wall area = 27.0 ft x 7.25 ft = 196 sq. ft.

Total absorption of walls is:

All-wood short wall: (85.2) x (0.25) = 21 Sabins for all-wood short wall

Wall with glass and corkboard (using the coefficient for curtain):

Glass: (1/3) x (85.2) x (0.08) = 2.26 rounded up to 2.3 Sabins

Curtain: (2/3) x (85.2) x (0.12) = 6.8 Sabins

Add these partial wall areas together: 2.3 Sabins + 6.8 Sabins = 9.1 Sabins for the glass/corkboard wall.

All-wood long walls absorption: 2 x 196 sq. ft. = 392 sq. ft. x (0.25) = 98 Sabins

Total for all walls: 21 Sabins + 9.1 Sabins + 98 Sabins = 128 Sabins

Note how much less the absorption is for the glass/corkboard wall than for the wood walls; materials do make a big difference, and so does frequency!

Total absorption of room at 250 Hz: 63 sabins (floor) + 143 Sabins (ceiling) + 128 sabins (walls) = 334 Sabins.

Now, we just plug into the reverb formula, and we get:

Volume of room = 27 ft x 11.75 ft x 7.25 ft = 2300 cu. ft.

T = (0.050) x (2300 cu. ft.) / (334 Sabins) = 0.34 sec. @ 250 Hz.

Let’s see how we do at 2000 Hz. We just take the above calculation, plug in the absorption coefficients for 2000 Hz instead of 250 Hz, and the rest stays the same. A few lines of math later, we have

Total absorption of room at 2000 Hz: 158.5 sabins (floor) + 285 Sabins (ceiling) + 53 sabins (walls) = 497 Sabins.

T = (0.050) x (2300 cu. ft.) / (497 Sabins) = 0.23 sec. @ 2000 Hz.

Looking at the results

Let me point out a few things about this result. I said at the beginning that if your reverb calculations were way off, you’d have to go back to the drawing board. Well, not so fast. Remember, I did the calculations for an empty room. My numbers came up a bit short of what I was shooting for, especially at the higher frequencies, but, here’s a few things that save the day. Anything with a hard surface that you add to the room will tend to boost the reverb time (keep sound alive via multiple reflections), especially at higher frequencies, with a few exceptions (shown in the chart in Berg & Stork).

My drumset, which has not a soft thing on it, my keyboard and its stand, all of my carts for gear, etc., will all serve to lengthen the reverb time of the room. What would tend to deaden (shorten) the time? Things like sofas, curtains (remember, I really have cork, which probably reflects more than curtains), books, clothing—anything soft. I don’t have much soft stuff in my studio, so I think the actual contents boost the numbers right up to where they should be, because the place sounds darn good. So keep that in mind when you calculate your reverb times.

Now, you might be saying, well, if you’re going to rationalize the number away, why bother in the first place? Good question. Answer: It depends how close you are to start with. I had my class invent a ridiculous room once. It had a concrete ceiling, a glass floor, and brick walls, or something like that, and they ended up with a reverb time of 6.2 seconds. There’s no way you’re going to rationalize that away with a few pieces of furniture!

The lesson is: if you are in the ballpark, think about what you are going to add to the room and which way these things will tend to push the coefficient. If they push it in the right direction, do it and leave things alone. If you are already off in the wrong direction and the equipment is going to make it more wrong, revisit some things, especially your choice of ceiling tile. They come in a wide variety of absorptions and the home improvement center can tell you what they are (and no, they won’t look at you like you’re from Mars), and it’s likely you can fix the problem just by changing the ceiling or doing a partial floor cover instead of full, and using some other material for the rest of the floor (i.e., instead of wall-to-wall carpet, how about an area rug on top of a Pergo floor?).

There are lots of ways to tweak the reverb time with things you put into the room, without a major redesign, if your number didn’t come out “right”. The bottom line is: how does the room sound?

Conclusion

You can see how knowing just a bit about room design can make the difference between having a room with nice, evenly spaced harmonics and a good reverb time for your kind of music, and just throwing something together in the space you have and then saying, “Hey, why is it so echoey in here (here here here)?” or “Why does everything sound so dead?”

If you’ve already made that mistake, start moving furniture! If the room is way too live, bring a sofa in there. If you can, bring in a bookshelf filled with books and magazines—they’re great at absorbing sound (and can shorten one dimension of your room by several inches if they’re floor to ceiling and wall to wall). Or get some acoustic foam and put it on the walls as needed.

If the room is too dead, take up the rug and put down a hard floor and check out your ceiling. If you have tapestries or curtains up, take them down and try blinds. There’s lots you can do to play with reverb time, but it’s best to get it right the first time!

Amy E. Bieber, Ph.D. is an Associate Professor of Physics at City University of New York, Bayside, and a recording musician and engineer.

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