© Jake Askeland

Abstract

Literature review of acoustical properties of various materials for use in treatment of a home studio. Focus is on inexpensive products and designs to correct the most common and problematic studio flaws with simple, do-it-yourself projects. Minimal discussion of physical mathematics.

Acoustical Treatment of Home Studios

The independent label or artist no longer struggles to find professional quality recording equipment at an affordable price; however, home studios still go acoustically untreated. Given that the recording industry been shifting toward smaller and less expensive organizations that are producing, recording, and mixing music, controlled and predictive acoustical designs for home studios with are now in great demand. Those who want better room acoustics are not necessarily the same people who want to learn all about sound physics. Musicians, it would seem, make the bulk of the growing population of home studio enthusiasts.

This research is therefore aimed at the home studio owner whose field is not engineering but art, a field which can require frugality when working alone or in small groups. It covers necessities to begin the process of treatment for any box-shaped room in a normal home or office setting. Limited discussion of math up through algebra is used to convey principles and define terms. When treating a room for the use of others who are paying well to use it, more should be taken into consideration than what is presented in this research.

This research begins with a discussion of sound physics used in room treatment such as absorption coefficients, cut-off frequencies, wave scattering, and modes. Following is a simple method for isolating the most common outside noises from penetrating the studio. Next, a set of materials commonly used to treat a room is laid out followed by a quick explanation of how best to use each material with minimal construction and cost. The set of materials includes fiberglass boards, block-type and perforated Helmholtz resonators, corner absorbers, and ceiling diffusers.

Basic Sound Physics Sound physics is traditionally studied with calculus and linear algebra to accurately predict the propagation of sound waves and their tendencies against various surfaces at various angles. However, for the average artist and home studio operator, simple definitions will do in

order to keep the intended effects of any treatments in mind. All calculations are estimates but are close enough to get the job done.

To start, a brief definition of wavelength and frequency are in order. A wavelength (ë) is the measure of length of a wave; in the case of this research it is in feet. It is inversely related to its corresponding frequency ( f ) and is given by the equation ë = (c / f ), where c is the speed of sound. A frequency is given by the equation ƒ = (c / ë) and is measured in Hz, which are cycles per second. That is, a wave with a frequency of 10 Hz will travel the distance of 10 of its own wavelength in 1 second. The term frequency is used in acoustics more frequently than wavelength. The term frequency response, used later on, refers to a range of frequencies at which something will respond such as the frequency response of a Shure SM57 microphone being more prominent at 1000 Hz.

When treating a room, the objective is the keep a fairly even frequency response throughout the room’s full volume so a microphone and instrument can be placed at any point and produce similar results to being placed anywhere else. In other words, the room becomes predictable. A metaphor by Philip Newell is that rooms are instruments that, in order to be played correctly, must be destroyed and rebuilt for predictability (1998, p. 30).

For the purposes of this research total destruction and rebuild are generally assumed to be out of reach, so instead absorption and diffusion of sound are needed in order to achieve the desired predictability. Absorption of sound, a less costly and time consuming objective, is described as the conversion of wave energy into heat in the air and in the walls (Morse, 1948, p. 385). After a wave is created by any means, be it a note on a trombone or an anvil falling to the ground, the energy of the wave will be absorbed until the wave no longer exists. In a perfectly open space with no walls and nothing but air and a sound wave propagating through it, the wave will continue until the friction between the air molecules dissolves it, which will take a very long time. Similarly, in a perfectly reverberant room (that is, one in which the wave looses no energy when it bounces from wall to wall), a wave will continue until that same friction in air stops it.

The difference is in the number of times this wave can be heard by an observer. In the open space, the wave only comes to a given point exactly one time and the sound of the wave is heard that one time for exactly what it is. In the room, the sound is heard possibly thousands of times, each time overlapping the last, making a (you guessed it) reverberation sound until it becomes inaudible.

Luckily, no room can be considered perfectly reverberant, and in most cases a room’s walls do absorb a great deal of wave energy. The variable describing just how absorptive a material is is called the absorption coefficient (a) which varies from 0 (perfectly reverberant) to 1 (perfectly absorptive). Morse (1948, p. 385) defines the absorption coefficient as the percent of energy absorbed by an object. For the purposes of this research, a will refer to the coefficient of audible and sub-audible frequencies absorbed. The difference may seem negligible but ‘energy’ can refer to any kind wave in any spectrum, whereas a will only include energy that our ears (and at very low frequencies, our hair follicles and skin) can detect.

The dimensions of a room determine its cutoff frequency and the modes at which frequencies can pile up (Shea & Everest, 2002, p. 3-4). The cutoff frequency is the frequency above which no modes will be transmitted (Morse, 1948, p. 308). Most home studios are six sided, having 4 walls, a ceiling, and a floor, each at 90 degree angles from one another. Such rooms, while not ideal for a professional recording studio, make the cutoff frequency and mode calculations much easier because there already exist a wealth of handy equations and web-based calculators for the do-it-yourselfer. There are even some free programs that can give a graphical representation of a room’s modes and where to dampen them.

Shea & Everest (2002) give the formula for cutoff frequency by Cf = 20,000 v(T/V) where Cf is the room’s cutoff frequency, T is the reverberation time in seconds, and V is the volume of the room (Length x Width x Height) in cubic feet (p. 263). But this doesn’t help when accurately calculating the reverberation time and can be extremely tedious for anyone but the architect who designed the room in the first place. An alternative calculator for the reverberation time can be found at http://www.mhsoft.nl/Rt60/Rt60.asp that, while making some assumptions about the building materials, does not require the user to know exactly what the room is made of and what lies beneath and above it.

Shea & Everest discuss that a room’s modes, determined by the ratio of length to width to height, are given by a series of calculations that lead to frequencies at which the walls will vibrate and generate reverberations. These reverberations occur as a wave bounces from one wall to another and back. Each reverberation works not only on its specific frequency (such as 141.2 Hz) but on all its multiples on upward (282.4 Hz - 2x, 423.6 Hz - 3x, etc.) and contribute to an unwanted coloration of the sound through 300 Hz. Such coloration occurs as each of the three axial modes (the three that interact between parallel walls and the floor and ceiling) generate similar or identical frequency modes (2002, p. 3-4), ergo a room with a ratio of 12:14:8 ft, which reduces to 1:1.167:0.667, has a pile-up of all three axial mode frequencies at 282.5 Hz (Wieczorek, 2004). Such calculations were made by an online calculator (see address under Wieczorek, M. in the references section).

Waves bouncing from wall to wall aren’t the only physics which dictate a room’s character. Wave scattering can either help the predictability of a room’s acoustics by averaging the reverberations around the entire room as has been more recently discovered (Peterson, 2001) or, as Morse puts it, it can hurt by distorting and interfering with the sound source. A wave is scattered when part of it bounces from an obstacle in a new direction and the rest continues on its original path (1948, p. 346).

Materials

A large part of making a room desirable for recording is keeping outside noise out. This is commonly referred to as isolation. The largest problems in isolation facing home studios are windows and doors, which can make up the bulk of openings and the uninsulated layers of a room. Double pane windows are known to insulate both thermally and acoustically and are easy to install. Standard home doors are too thin to absorb anything but the slightest of noises and will let neighbors now about each and every take that is made, but 1¾” solid core doors have a 33 dB transmission loss in the mid range (approx. 500 Hz) and weatherstripping can be added to complete the room’s isolation (Shea & Everest, 2002, p. 17). Both take less effort than most other parts of acoustical treatments for a home studios and professional studios alike. In a traditional studio, however, sound locks are common practice. Sound locks are hallways that have solid doors and airtight seals for three of more openings. They open up into the the control room(s), the studio(s), and the rooms outside such as a parlor so that sound doesn’t travel between each room during the recording process.

Once a room has been isolated to a satisfying degree, the objective is then to dampen trouble frequencies caused by modal pile-up below the cutoff frequency and to create a fairly predictable acoustical environment throughout the audible spectrum wherever a microphone might be placed. The smaller the room, the less treatment material might be necessary, the larger the room, the fewer frequencies will be a problem for modal compensation (Shea & Everest, 2002).

In order to catch a specific modal frequency, a Helmholtz resonator is built and tuned to that frequency (Shea & Everest, 2002, p 245; Sapoval, Haeberle’, & Russ, 1997, p. 2014). By the German name, it might sound complicated and expensive to design and build a working resonator but there are plenty of ready-made designs using materials costing less than $50. There is no great

difference between perforated and slit-type resonators, but the method of finding each one’s peak absorption frequency and tuning it to the correct peak is different (Shea & Everest, 2002, p. 246).

If the modal frequencies to be controlled are floor-axis based or for any other reason should be structurally capable of withstanding physical force, a block-type resonator will be better equipped to handle the conditions. Block-type resonators are constructed by making a box with a port hole which is of a diameter that resonates at the desired peak frequency (Shea & Everest, 2002, p. 245). When building a block-type resonator, using a neck shape resembling that of a funnel over the port hole will control high frequency absorption and still allow for low end absorption (Sakamoto, 2000, p. 14-15). Type R proprietary Soundblox use a block and funnel design which absorb well at 125-250 Hz and don’t absorb much past 500 Hz (Shea & Everest, 2002, p. 252).

If the modes include more than one wall-axis, a perforated panel with an absorbent material such as fiberglass will act as a Helmholtz resonator. For the home studio owner, a preferred perforation equation is f = 200 v(p/(d)(t)) where f is the absorbed frequency, p is the percent area of the panel covered in perforations, t is the panel thickness + (0.8)(hole diameter), and d is the air space depth behind the panel in inches. This will suffice when building a tried and true perforated resonator; however, new absorbers called microperforated panels (MPPs) are seen as attractive alternatives for the latest sound insulation systems (Sakagami, Morimoto, & Yairi, 2005, p. 204). Sakagami, et al. continue that by using acrylic glass panels of significant mass, such as 2 kg/m2, and by placing holes at distances of 3.5 mm from one another, absorption can be controlled via hole diameter as in standard perforation techniques. The difference is a 0.2 mm diameter will cover a broad spectrum from 125 Hz to 2 kHz (a = 0.35) while a 0.7 mm diameter will focus absorption at 500 Hz (a = 0.95). The absorption spectrum and a vary respectively between the two diameters (2005, p. 205).

Now that the modal frequencies are dealt with, any further treatment for predictability will be relatively simple. With newly abundant commercial products for sound absorption, it could be confusing to the home studio owner as to which products are necessarily expensive and which products can be fabricated by hand with less expensive materials. Numerous foams are now available that require very little effort and do a good job at absorption with a generous frequency range for a premium cost of about $3.90 per square foot (Auralex 2″ SonoFlat Studiofoam). The same foams can reach a necessary depth of 125 Hz at a respectable á when doubled up upon each other for a total cost of about $7.80 per square foot. For reference, this would be over $1300 of foam for the walls of the previous example room’s dimensions (12 x 14 ft).

On the other hand, Shea and Everest (2002) explain that porous foams are more expensive and only slightly more absorbent than their fiberglass counterparts (p. 31). So the same $1300 job can be done with fiberglass type 703 (which is just a part number by one company that produces 3 lb/ft2 fiberglass (Shea & Everest, 2002, p. 31)) panels for under $300. The only difference is the preparation needed for the fiberglass (Shea & Everest, 2002, p. 255). Fiberglass can be flaky and the fibers are irritative to the skin and harmful to the eyes so care must be taken when handling and light weight, loose cloth such as burlap should be used to cover each panel (p. 255).

For placement of the paneling, several factors can affect the sound absorption characteristics and should be taken into account when deciding upon a strategy for the absorption at various frequencies. The best practice in such strategies is to absorb on all frequencies evenly when all is said and done and then to allow for adjustment to different situations. Situations that might come up are vocals that need to sound “sweeter” in the mid range or bass drums that are acting on a mode that was not tuned for (Greg Demascio, personal communication, June 28, 2005). For the paneling described above, keep in mind that for panels put directly on a wall, an unsupported panel cannot reach the lower frequencies; a supported panel’s frequency absorptionis directly related to the stiffness of its support (fiberglass mounted on a drape will only absorb the frequencies the drape will); and a porous material, when thicker than a given wavelength, will completely absorb the wave’s energy (Morse, 1948, p. 362-364). For general practice, remember that walls are perpendicular to the most coloring of sound waves so to put something directly on a wall will maintain that perpendicularity. The absorption coefficient of a material with an uneven surface or a material on an incline is greater than that of a material with an even surface on a material perpendicular to the sound wave (Skibata & Yasuro, 2003, p. 155). This is especially useful when damping corners.

Corner absorbers, due to the acoustic nature of modes, effectively absorb on all modes in a room (Shea & Everest, 2002, p. 31). A design put into practice at Paul Stubblebine Mastering of San Francisco is to place tall sheets of fiberglass, covered with a loose finishing cloth in the corners of their mastering rooms at an angle so that the sheets are not perpendicular to any wall, nor are they strait up and down.

For ceiling treatment, Shea & Everest (2002) suggest anything that will absorb well what the floor is not absorbing should be used on the ceiling (p. 144). This sounds simpler than it usually is. Carpet absorbs increasingly with frequency, leaving the low end almost completely to reflect off whatever is beneath it (p. 251) so if carpet is on top of anything but a good low-end absorber, the ceiling should pick up the slack. So far, materials discussed that can do such absorption and that aren’t too bulky to hang or attach to a ceiling are 2-ply 2” 3lb/ft2 fiberglass panels and perforated resonators. Shea & Everest (2002, p. 144) don’t suggest this in most cases only because its significantly harder than putting absorbing materials on the walls.

Going beyond absorption for the ceiling, diffusion scatters waves evenly about the room, making them more equally present at every point and therefor more predictable. There are dozens of prefabricated products to handle this and it might be one place where the do-it-yourselfer callsthe professionals. Peterson says reflection phase grating type diffusers create the most predictable levels which have been described to make walls seem nonexistent. The key is in the many depths of the various panels that make up the ceiling (Peterson, 2001). In these types of diffusers, a cross section looks a lot like a bar graph where each bar is of a different length than its neighbor but a repeating pattern can be seen across the whole. That pattern is called a quadratic residue sequence (Shea & Everest, 2002, p. 239; Peterson, 2001). The standard now in quadratic residue sequences is as follows: 1, 4, 9, 16, 8, 2, 15, 13, 13, 15, 2, 8, 16, 9, 4, 1; where each number in the sequence is multiplied by the longest wavelength to be diffused, giving the depth of each piece of the diffuser (Shea & Everest, 2002, p. 239; Peterson, 2001). If something more simple and within reach to the home studio owner is desired, small plastic diffusers that fit into the square partitions in office ceilings are commercially available at around $50 and using one such diffuser every so often in a pattern will help considerably, especially if the studio happens to be in some kind of office space where sound below the high frequencies will penetrate the thin ceiling tiles.

Quick and Dirty For the very budget conscious and time deprived home studio owner, a cheap and effective way to get a studio isolated with barely adequately treatment is certainly possible. A suggestion is to buy rolls of fiberglass wool of 3lb/ft2 and attach them to the walls and ceiling with staples and consider the solid core doors and double paned windows further down the line.

For the rest, a great many books, articles, calculators, and helpful engineers are available and the quantity and quality of all are increasing with time. For further reading, see Shea & Everest in the References section.

References

Morse, P. M. (1948). Vibration and sound (2nd ed.). New York: McGraw-Hill.

Newell, P. R. (1998). Recording Spaces. Woburn, MA: Focal Press.

Peterson, I. (2001). Acoustic Residues. Science News 160(1). Retrieved June 30, 2005, from http://www.sciencenews.org/articles/20010707/mathtrek.asp Sakagami, K., Morimoto, M., & Yairi, M. (2005). A note on the effect of vibration of a microperforated panel on its sound absorption characteristics. Acoustical Science and Technology, 26(2), 204-207.

Sakamoto, S., Mukai, H., & Tachibana, H. (2000). Numerical study on sound absorption characteristics of resonance-type brick/block walls. Journal of Acoustical Society of Japan, 21(1), 9-15.

Sapoval, B., Haeberle’, O., & Russ, S. (1997). Acoustical properties of irregular and fractal cavities. Journal of the Acoustical Society of America, 102(4), 2014.

Shea, M. & Everest, F. A. (2002). How to build a small budget recording studio from scratch (3rd ed.). New York: McGraw-Hill.

Shibata, K., & Yasuro, H. (2003). Numerical analysis of sound absorption characteristics of the sound absorbing wedge. Acoustical Science and Technology, 24(3), 155-156.

Wieczorek, M. (2004). Room mode / standing wave calculator. Retrieved June 25, 2005, from http://www.marktaw.com/recording/Acoustics/RoomModeStandingWaveCalcu.html