A New Approach to Small Room Acoustics

From Electronic Musician, April 2004

..MORE THAN JUST MODES..

More RealTraps Articles

Sometimes conventional wisdom is wrong. Here's the real truth about small room acoustics and how it affects the music you record and mix.

 

 

 

 

"Contrary to popular belief, all small rooms have peaks and severe nulls at all low frequencies, not just the mode frequencies determined by the room's dimensions."

 

 

 

 

 

Click to see a larger version
Figure 1: This frequency response was plotted at 1 Hz intervals in a control room measuring 16 by 10 feet, 7-1/2 feet high. As horrible as it looks, this is typical for small untreated rooms. Click the image for a larger version.

 

 

 

 

 

"One of the great ironies of acoustics is that thick rigid walls that improve isolation between rooms cause more acoustic problems within the rooms."

By Ethan Winer

These days more and more recording and mixing is done in rooms that are very small by previous professional standards. This includes not only amateurs and weekend engineers working in their home studios but also real professionals doing real music projects for major labels. However, much of the conventional wisdom about room acoustics, measurement, and treatment does not take into account the unique behavior of small rooms. This article explains two important acoustic principles relating to low frequencies in small rooms, which are often misunderstood or overlooked entirely.

Contrary to popular belief, all small rooms have peaks and severe nulls at all low frequencies, not just the mode frequencies determined by the room's dimensions. This has a profound effect on the way low frequency acoustic problems should be approached. For any given low frequency, there will be places in the room where a peak exists, and others where a deep null exists. Likewise, for any given location in the room, there will be frequencies with a peak in the response and others with a null. Specifically, a null occurs at a distance from most boundaries (walls, floor, and ceiling) equal to 1/4 the wavelength of the frequency [1]. Other nulls occur at odd multiples of that distance: 3/4 wavelengths, 5/4, and so forth. Similarly, peaks occur at 2/4 wavelengths, 4/4, 6/4, etc. Note that the angle at which the waves strike the boundary influences this distance. Top

Some boundaries have stronger peaks and nulls than others, due to multiple reflected waves coming from different directions and combining in the air. In fact, all acoustic problems in all rooms are caused by reflections. Because the peaks and nulls in small rooms occur at regularly spaced frequency intervals, the net result can be considered a type of comb filter. This is exactly how flanger and phaser effects work, except in this case the filtering happens acoustically in the air as the waves collide, reinforcing or canceling each other. The general term for this phenomenon is acoustic interference.

This effect is much more pronounced in small rooms than larger ones because the walls are closer together and so the reflections are stronger. However, the strength of the reflections also depends on the density of the walls, with rigid walls reflecting more and to lower frequencies. Indeed, the worst environment for a home studio is a basement because cement walls are more rigid than standard sheet rock walls. One of the great ironies of acoustics is that thick rigid walls that improve isolation between rooms cause more acoustic problems within the rooms. With standard walls made of one layer of sheet rock, the lowest frequencies pass through to some extent, and are also partly absorbed when the wall vibrates in sympathy. Walls made of cement or multiple layers of sheet rock reflect more and to lower frequencies, thereby increasing the damage caused by acoustic interference. Top

As I explained earlier, peaks and nulls occur at predictable quarter wavelength distances from every room boundary. The nulls are often strongest at the rear wall because the loudspeaker's wavefront traveling the length of the room is strongest in that direction. But other reflections occur at other boundaries, and they combine in and out of phase to bolster or reduce the quarter wavelength nulls. In order to create a deep null, the opposing wavefronts must be nearly identical in level. It takes very little contribution from an errant reflection arriving from somewhere else to disturb the precise balance needed to create a deep null.

If you want to experiment with this in your own control room using a sine wave generator and tape measure, understand that you can't just place a mike or your ear some distance from a wall and expect to find a deep null. You also have to move up and down, and left and right, to find the best place where the null is not influenced by a competing reflection off the floor, ceiling, or another wall. Top

In most rooms the peaks caused by acoustic interference are usually less than 6 dB, but the nulls are typically 30 dB or more deep, as you can see in Figure 1 above. In fact, most people first become aware of bass problems in their rooms when they notice a lack of bass at the mix position compared to other locations. A slight peak is not nearly as noticeable or damaging as a deep null. Further, many nulls have a very narrow bandwidth - and this brings us to the second issue. Top

Click to see a larger version
RealTraps partner Doug Ferrara prepares to measure a typical project studio control room. Click the image for a larger version.

 

 

 

 

Click to see a larger version
Any DAW program can measure a room's response without special test gear. This Sonar project plays 260 sine waves in 1 Hz increments from 40 to 300 Hz. Each tone on the first track sustains for one second and is played through the speakers. A microphone at the mix position is then recorded on the second track. This reveals the room's response at each frequency, which you can also read from the second track's playback level meter. Click the image for a larger version.
FORGET EVERYTHING YOU KNOW ABOUT REAL TIME ANALYSIS

Standard real time room analysis using pink noise to measure the frequency response in third octave bands completely misses these peaks and nulls. When pink noise is analyzed in bands, the levels of all frequencies within each band are averaged together. Even measuring at 1/12th octave spacing is far too coarse to see the true room response. I have observed peaks and adjacent nulls less than 1/12th octave apart in many small rooms. So depending on what frequencies are measured versus at what frequencies the peaks and nulls occur where you place the measuring microphone, it's likely that a room will appear perfectly flat when in fact there exist many large aberrations that are completely hidden.

One excellent way to measure the true low frequency response of a room, without needing special equipment or analysis software, is to play low frequency sine waves and measure the result at various locations in the room. This is not an unreasonable test because all music is ultimately made up of sine waves that sustain for some length of time. When a bass player holds a long note in a slow ballad, that note contains mainly two sine waves: the fundamental pitch and its second harmonic. Likewise, kick drums produce mostly sine waves, though the waves often fade quickly and are also accompanied by the click sound of the beater against the drum head. Even cymbals, maracas, and every other musical instrument create sound composed entirely of sine waves, even if those waves sustain only briefly. Top

Even if you measure the room using a bandwidth of one Hz - whether with pink noise, impulses, or sine waves - there's another issue to consider: The physical size of acoustic nulls is often extremely tiny, so the notion of a mixing "sweet spot" is meaningless unless you're willing to clamp your head in a vise. In one test I located the physical center of a deep null at 100 Hz in my own control room. I then moved the microphone four inches to the side - equivalent to turning your head a little - and the level rose by 15 dB. When the mike was 18 inches from the null center the level was 20 dB higher.

If you measure a room's response using sine waves 1 Hz apart, you'll still have to measure every frequency at dozens of locations within a cubic foot or two of the mix position to get the true picture. One saving factor is that our ears are several inches apart. So when one ear is in the center of a very deep null for a given frequency, the other ear is likely to be out of that null, though perhaps it will be in the center of another. The severity, narrow bandwidth (high Q), and small physical size of acoustic nulls is also the main reason EQ can never correct low frequency problems in small rooms. Whatever you do to flatten the response in one location will surely make things much worse somewhere else nearby. Top

Added after publication: The Sonar project shown above can be downloaded for free at the RealTraps Videos page (22 MB). However, if you are serious about room analysis I recommend the fabulous ETF program from Acoustisoft. It performs all of the important tests needed to fully analyze any room, yet it's very affordable.

SIDEBAR: UNDERSTANDING NODES, MODES, AND STANDING WAVES

Many people believe that room acoustics is a complicated subject, understood only by those with a Ph.D. in math or physics. However, the behavior of sound waves in small rooms is actually pretty simple, at least for the purpose here of solving problems common to recording studios and control rooms. As explained in the main text, all acoustic anomalies are caused by reflections off the walls, floor, and ceiling. However, I distinguish between problems caused by reflections at low frequencies - below about 300 Hz - and those at mid and high frequencies. Above 300 Hz reflections are perceived mainly as echoes, ambience, and reverb. Below 300 Hz the skewed frequency response typified by Figure 1 above is a much bigger problem. In all cases, waves bounce around in a room much like a cue ball on a pool table. In this case, though, they can bounce around in three dimensions.

Click to see a larger version
Figure 2: A node occurs when direct and reflected waves that are out of phase with each other collide in the air. Click the image for a larger version.

Nodes, modes, and standing waves are three key properties that apply to all rooms, and they are closely related.

A node is just a fancy word for a place in the room where a null or dip in the frequency response occurs. A node is caused when two waves meet in the air and combine out of phase, as shown in Figure 2. In a typical case, waves emitted from a loudspeaker reach a wall and are reflected back into the room. At some distance from the wall, the original wave will have a positive pressure while the reflected wave is negative, or vice versa. When the reflected wave is exactly equal in level and also exactly 180 degrees out of phase with the original, the waves will cancel completely at that particular location. At other levels and phase relationships the waves will cancel less. (And when they're in phase, they increase in level by some amount instead of canceling.) In practice, total cancellation never occurs because no wall is 100% reflective at any frequency.

A mode is simply a natural resonance that occurs in a room, and the frequency of the resonance depends on the room dimensions. For a typical rectangular room, there are three fundamental mode frequencies. One for the length, another for the width, and yet another for the height. Sound travels at a speed of approximately 1130 feet per second, so the resonant frequency between two opposite walls can be determined by this formula, where Feet is the distance from one wall to the other:

1130
Frequency =
Feet x 2

Twice the distance is used because a wave travels from one side of the room and back to complete one cycle. In truth, each dimension has a series of modes because higher frequencies can also occupy the same distance. That is, wall spacing that exactly fits one cycle of 70 Hz also accommodates two cycles of 140 Hz, three cycles of 210 Hz, and so forth.

The most common type of mode is the axial mode, which occurs between two opposing surfaces, such as the floor and ceiling. There are also tangential and oblique modes, which are weaker and thus have less impact on the room's response. Tangential modes complete one or more cycles after bouncing off four room surfaces - literally like a cue ball going around a pool table in a diamond shape. Oblique modes are weaker still and bounce off all six surfaces to complete one or more cycles.

A standing wave is a wave that's not moving - it is literally standing still. Standing waves occur when two equal yet opposite waves arrive from different directions and collide. A few inches away the waves are traveling toward each other. But at the one precise location where the wavefronts meet, there's no motion, much like the isometric exercise of pushing your hands together. Some people wrongly consider modes and standing waves to be the same thing because standing waves can occur at modal frequencies. But they are not at all the same because one is a wave and the other, a mode, is merely a propensity to vibrate. Further, opposing waves can create peaks and nulls at nearly any frequency in any room, not just those frequencies that correspond to the room dimensions.

SO WHAT DOES THIS ALL MEAN?

The old-school method of low frequency acoustic treatment is to calculate the room's modes based on its dimensions, and then design custom bass traps that target those specific frequencies. This is inadequate because it addresses only the modal frequencies, ignoring the peaks and nulls caused by acoustic interference that occur at all other low frequencies. Further, even if you consider only the first five axial modes for each dimension, that still requires building bass traps for as many as fifteen different frequencies! Therefore, a much better solution is to use broadband absorption because that flattens the response throughout the entire low frequency range.

In some severe cases - for example, with a room that's 8x8x8 feet - it could be useful to complement broadband absorption with traps that target the enormous resonance that exists when all three dimensions are the same. In this case the resonance is at 70 Hz. But similar resonances exist at all multiples of 70 Hz, so broadband trapping is still needed since the related frequencies must also be treated. (And any room that's only 8x8x8 feet probably doesn't have space for a sufficient number of traps that target such a low frequency.) Top

Another important point, which again defies conventional wisdom, is dispelling the myth that you can learn to make great mixes in an untreated room. The biggest problem most people have when mixing is getting the bass levels correct. Often a mix that sounds correct in your control room will sound boomy when played elsewhere. Most small rooms have a deep null at the mix position between about 80 and 120 Hz. (The exact frequency depends largely on how far you sit from the rear wall.) So you tend to mix with too much bass to compensate for what you're hearing. When a mix can be made to sound good both inside and outside your control room it's said to be "portable."

I often see people advise playing a commercial CD of the same type of music as you're mixing, with the goal of matching the bass levels to obtain a portable mix. The problem with this approach is matching bass levels with a commercial CD works only if both songs are in exactly the same key! Let's say your song is in the key of E, and your room is similar to that shown in Figure 1. Whether the bass is playing a low E or the octave above, either the fundamental or all-important second harmonic will align with the deep null at 82 Hz making the bass seem very thin even though it really isn't. But if the reference song is in the key of A, either the low A or the octave above will align with the enormous peak in the response. With these two particular keys, anyway, trying to make a well balanced mix by matching bass levels is doomed to fail. Top

I visit a lot of audio newsgroups and web forums, and people often ask if they should buy a subwoofer to improve their ability to mix. While a subwoofer can help compensate for inadequate loudspeakers, it will not solve the problem of an irregular response caused by acoustic interference. Often a subwoofer just compounds and hides the problem. In truth, even if your monitor speakers cost as much as your house, the response you hear will still vary by 30 or more dB in a typical small untreated room.

OVER, BUT NOT OUT

In this article I explained some of the common acoustic problems facing owners of personal studios, and showed why conventional thinking doesn't always apply to the small rooms that are often used these days. As you've seen, small room acoustics is not really that complicated, and all problems are caused by waves reflecting off the room boundaries. In a future article I'll describe the solutions - mainly bass traps and other acoustic treatment - and explain what types work best, how much treatment is needed, and where it should be placed for maximum benefit. Top

Until then, I'll leave you with some conventional wisdom that is valid, even though few people understand why. Many folks who don't have proper acoustic treatment have learned to play mixes in their cars, to get a better sense of the bass levels. Of course, most car stereos are a poor second to a good pair of monitor speakers. Yet this method works surprisingly well, discounting the nuisance of having to keep burning CDRs to bring to your car. Many people think a car is good a place to assess mixes because we spend so much time listening there. But we listen to our "good" loudspeakers a lot too, no?

As you know by now, acoustic reflections cause a series of peaks and dips throughout the entire low frequency range. This is much worse than an overall lack of bass, or overall increase in bass, which you could more easily compensate for. For whatever ills most car stereos have, they do not usually suffer as much from acoustic comb filtering because a lot of the low frequency energy passes right through the lightweight walls to the outside. And by passing through the walls instead of being reflected, the low end response is more uniform than in many rooms. It's easy to prove this to yourself: Start some bass-heavy music playing fairly loudly in your car, then roll up all the windows and get out of the car. All you hear outside the car is the bass that escaped through the car walls and windows instead of being reflected. Top

Note that some car stereos, and many boomboxes too, have a permanent "loudness" type compensating boost at the upper bass range. This is done to fool inexperienced listeners into thinking the system has more bass than it really does. If your car or boombox is like that, you'll have trouble hearing bass accurately. But many car stereos, including the stock stereo in my aging '93 Camry, have a surprisingly flat and extended low end.

References:

[1] Bass Waves in the Control Room, by Wes Lachot, first published in TapeOp magazine.

Ethan Winer is based in Connecticut where he and partner Doug Ferrara design bass traps and other acoustic treatment for RealTraps. Visit them at www.realtraps.com.

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