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Many people enjoy the body-vibrating bass experienced in the finest concert halls (like Boston’s Symphony Hall) and in a few movie theaters. However, this experience has proved exceptionally difficult to bring home. In fact, the acoustics of a normal home listening room make it nearly impossible to secure flat frequency response in the important range of 20 to 400 Hz at the listening position.
Acoustical factors that influence the amount and perception of bass in a listening room include:
Although it is impossible to separate these effects in a real room, as all of them act simultaneously on the sound traveling from the speakers to the listener’s ears, they are easier to understand when analyzed separately.
Physically, sound consists of cyclic air movements, which produce pressure waves and velocity waves that are correlated as shown in Fig. 1. At the point where the pressure is maximum or minimum, the velocity is zero (that is, the net velocity of the air molecules near this point in space is zero); where the air molecular velocity peaks, the pressure differential is zero. (By pressure differential, we mean the difference between the pressure at that point and the nominal atmospheric pressure.)
Complex sounds, such as music or speech, can be viewed as ever-changing linear combinations of individual frequencies of various amplitudes. Therefore, a discussion of single-frequency sine wave patterns will make the explanation easier and can be extrapolated to cover complex sounds.
A sound’s frequency is marked off in cycles per second (now called hertz, or Hz, after the 19th-century German physicist Heinrich Hertz), which is how often the sine wave pattern recurs each second. A corollary to frequency is wavelength— how far a single cycle of the sound travels. This is a simple function of the frequency and the speed of sound in air, which is approximately 1,130 feet per second. The higher the frequency, the less time between reversals and thus the shorter the wavelength (Fig. 2).
Sound pressure level (SPL, measured in decibels, or dB) is a time-aver aged calculation of the “effective” amplitude (see Fig. 3) of the sound pressure relative to a very low reference level (0.0002 microbar) that approximates the mid-frequency threshold of human hearing.
From the Back Cover
No one can touch the Master ...No other book even comes close to legendary acoustical scientist F. Alton Everest's Master Handbook of Acoustics for a friendly, practice-oriented tour of acoustical principles. This readable yet authoritative guide tenderizes a tough subject so that audio buffs can apply leading-edge acoustical thought and design in their own home recording studios and listening rooms.Keeping his target audience of hobbyists, electronics enthusiasts, and audiophiles always in mind, the author makes the science of sound interesting and understandable. Only someone who understands acoustics as well as Everest – Senior Member of the Society of Motion Picture and Television Engineers, the Acoustical Society of America, and the IEEE -- could explain these principles so simply, informally, and with such relevance to home projects.
Short on mathematical derivations and long on easy-reading translations of difficult technical subjects, F. Alton Everest's Master Handbook of Acoustics is a rewarding piece of prose that can help you elevate any audio project to a higher standard. An inexhaustible source of ideas, inspiration, and techniques, it's a classic work that every audiophile wants to own. This book is a true keeper.
TURN SCIENCE INTO ART
For those who love electronics and high-end listening and recording,
this book is the key to the kingdom, unlocking the theory that lets you:
WITH CONTRIBUTIONS FROM--Geoff Goacher, Acoustical Research AssociatesPeter D'Antonio, President & CEO, RPG Diffusor Systems
About the Author
axial modal frequencies, independent loudspeaker, furring lumber, image source model, home listening rooms, binaural impulse responses, lowest axial mode, residue diffusor, nonrectangular room, perforated panel absorbers, perforation percentage, bass absorption, quadratic residue sequence, reverberation time, sound pressure distribution, higher audio frequencies, separation recording, voice colorations, room modes, simplex routine, reflection phase grating, room resonances, acoustic distortion, oblique modes, glass fiber board
Sound emanating from any source (our mouths, speakers, noisy machines, etc.) travels through air, all the while maintaining its complex shape of pressure over time and distance. When the sound strikes a surface, it begins traveling in a new direction, but the shape of the pressure wave continues unchanged, except for losses into or through the surface, which we’ll get to later.
When a wave traveling in one direction crosses the path of a wave traveling in an other directions, their instantaneous pressures (relative to nominal air pressure) reinforce or cancel, depending on their values. For example, if both are positive (or negative) relative to atmospheric pressure, they will sum to a larger pressure differential. But if one is positive and the other negative, they will sum to a smaller pressure differential (zero if the two happen to have the same amplitude at that time and place).
They make visualization a little easier, assume that the speaker is at one surface. For a given spacing between two surfaces, there is. frequency for which that distance is equal to one the wave length (see Fig. 4); :in other words, with the positive peak pressure point at the speaker, the negative peak pressure point in the waveform is at the other wall. The result is that as the sound continues, and the reflection off the far surface returns to the speaker, the next positive peak pressure point is back at the speaker. Thus, the forward and return waves rein force each other all along the path (except at the zero-crossing point, where there is nothing to reinforce). This is known as a resonance, or standing wave, and at any frequency that creates such a resonance, there will always be maximum pressure differential at the two opposing surfaces. And for this fundamental resonance, where the surfaces are a half-wavelength apart, the pres sure differential will drop to zero midway between them.
While any waves will interact where they intersect, only those with a specific relationship to the surface spacing will rein force all along their path, no matter how many times they bounce back and forth between the two surfaces. The rest of the interactions are random and average out to no net effect.
For a given dimension, resonance also occurs for each multiple of the fundamental frequency, with the number of reinforcement peaks and cancellation nulls proportional to the multiplication factor. This yields a series of maximally affected frequencies, with twice as many in each octave as in the one below.
This effect occurs no matter where the speaker is with respect to the surfaces! In fact, it occurs for each pair of opposite surfaces—wall-to-wall and ceiling-to-floor. Thus, in a convention al rectangular room there are three series of axial standing waves—one series for each pair of opposite surfaces—and the fundamental frequency of each series can be calculated by the formula f=565/d, where d is the distance in feet between the surfaces.
There is more to the story, however. Measurements and analysis have validated the original work of Philip M. Morse and Richard H. Bolt (of Bolt, Beranek and Newman), who 45 years ago described three types of standing waves: axial, involving only a single pair of opposite surfaces; tangential, which, like a four- cushion billiard shot, involve the four successively adjacent surfaces of a closed rectangle; and oblique, which involve all six room surfaces.
Morse and Bolt noted that there is a difference in relative energy for each type of standing wave, such that, for a given pressure amplitude, an axial wave has twice the energy of a tangential wave and four times that of an oblique wave.
E. Alton Everest and many others have concluded from this that tangential and oblique resonances can be effectively ignored, since their energy is so much lower than that of the axial waves. However, Morse and Bolt also stated the following (emphasis added):
“Axial waves are made up of two traveling waves propagated parallel to one axis and striking only two walls. Tangential waves are built up of four traveling waves, reflecting from four walls and moving parallel to two walls. Oblique waves are built up of eight traveling waves reflecting from all six walls.” So the reduction in energy per wave for the tangential and oblique resonances is exactly offset by the increase in the number of waves, making the total room energy contribution of each type of standing wave the same. This finding conflicts with Everest’s assumption but seems to agree with experimental data collected by a number of well-respected researchers. Thus, a calculated room resonance series based only on axial standing waves is incomplete and will lead to erroneous conclusions.
What all of this means is that regardless of where the speakers are located, there is a set of standing waves based on the room dimensions that will cause peaks and dips in the frequency response at every point in the three-dimensional space of the room, and at different frequencies these peaks and dips will occur at different locations.
ROOM DIMENSION RATIOS
Now that we know that standing waves affect the frequency response and that the standing-wave frequencies can be calculated from room dimensions, the question arises whether there is some optimum ratio of room dimensions to minimize the sonic impact of standing waves. In other words, what ratios will yield the most even distribution of standing-wave frequencies?
The most widely accepted work on this subject is that of M. M. Louden, which followed on that of Morse and Bolt. Louden’s most highly recommended room dimension ratio is 1:1.4:1.9, which for a room with an 8-foot ceiling would be 8 x 11.2 x 15.2 feet. This agrees with the recommendations of Bolt, Ludwig W. Sepmeyer, and Tomlinson M. Holman and of the ITU-BR (International Telecommunications Union—Radio communications Assembly, formerly the CCIR). The ITU BR also concludes that the criteria used to determine a good listening room for two-channel stereo are also valid for 5.1-channel surround.
Over a fairly wide range of room sizes and all else being equal, a larger room will yield better bass response than a smaller one. The exception, discussed later, is a very small volume (such as an automobile’s interior), which forms a low-frequency "pressure pot."
The main advantage of a large room is that it will tend to have a lower Schroeder frequency than a smaller room, which in turn will tend to make the frequency response smooth over a wider range. The Schroeder frequency is the approximate frequency above which the room resonances (standing waves) are so closely spaced that they do not substantially affect the sound. Thus, it is necessary to pay serious attention only to the dimensionally determined resonances below the Schroeder frequency, which is a function of room volume and reverberation time. The larger the room or the shorter the reverberation time, the lower the Schroeder frequency.
The more rigid a room’s surfaces, the better it will maintain low frequencies. Roy Allison and others have de scribed how “soft” walls, “soft” ceilings, “soft” floors, padded furniture, room dividers, and openings (doors or windows) affect the severity and “Q” (bandwidth) of response peaks and dips in a room.
We’re all familiar with loud bass coming from a closed-up car idling next to us at a traffic light. We also are aware of the bass thumping through the walls from a neigh boring apartment, especially late at night when we want to sleep.
Sound is vibrating air molecules. When these molecules strike a surface, they transfer energy to it, causing the surface to vibrate. The surface reflects some of the energy back into the room and dissipates some of it as heat, but the rest is transmitted through the surface into the adjoining area, whether that is a room or the outside air. The less rigid the surface, the higher the percentage of the energy transmitted to the other side. Because of the mass and dimensions of typical room surfaces and the longer wavelengths of lower frequencies, bass tend to be transmitted through these surface much more easily than high frequencies, attenuating bass inside the listening room. Also, and for all the same reasons, doors and windows cause a greater bass loss from a room than the walls. This is why, all other factors being equal, a listening room in a cellar will usually have stronger bass than a room on an upper floor.
BOUNDARY EFFECTS AND SPEAKER PLACEMENT
Apart from his work as a speaker de signer Roy Allison is best known for his investigations into the sonic effects of room dimension ratios and boundary augmentation of loudspeaker output. In particular, he quantified what has be come known as the Allison effect: a predictable dip, or suckout, in the low-frequency response that is determined by the distance from the center of the driver to each room boundary. This effect is notice able only for the woofer, since for the distances normally involved, the frequencies affected are usually around 150 to 200 Hz.
For a given distance from the speaker to one surface, there is a 1-dB dip at the maximally affected frequency. For a speaker that is the same distance from each of two surfaces, such as the floor and the wall behind the speaker, the dip is around 3 dB. If, by some chance, the speaker is the same distance from each of the nearest three surfaces (i.e., in a corner), the suck-out is approximately 11 dB.
Psycho-acoustically, a narrow bass notch (suck-out) is less objectionable than a broad- spectrum boost (ignoring the fact that a lot of us are perfectly happy with bass boost, even though it moves us away from high fidelity!). But such boost is another product of boundary interaction. As the frequency gets lower and the wavelength becomes longer than about ten times the distance from the speaker to the nearest surface, the room becomes a pressure pot and output is entirely displacement-limited. Exact location is irrelevant, because at longer wavelengths the woofer is acoustically “dose” to the room boundary. As the distance to the nearest surface meets this criterion, there is a shelving bass boost of about 3 dB. As the next surface comes into play, a total boost of around 6 dB occurs. When the speaker is close enough to all three of the nearest surfaces, the bass boost is 9 dB. As Allison makes clear, this effect has two causes. It reduces the angle into which the speaker radiates—from a full sphere (suspended in open air), to a half sphere (on the floor), to a quarter sphere (also at one wall), and then to one-eighth sphere (near a corner). And nearby surfaces improve the cone’s “bite” on the air, which increases speaker efficiency.
For a single-surface effect, the boost-to-dip ratio is 4 dB; for two surfaces the same distance from the speaker, it is 9 dB; for three surfaces, it is an amazing 20 dB from shelving boost level to the pit of the suckout! This is why it is best to have the front of the speaker flush with the wall (or, in the case of bookshelf speakers, buried in a shelf full of books). Given that this is unlikely for many situations and speakers, it is best that the speaker be different distances from the floor, each wall, and the ceiling and that none of the distances be multiples of any other. A simplistic formula that is fairly effective is: B2= A x C, where A is the distance to the nearest boundary, B is the distance to the next nearest boundary, and C is the third distance; only in rare cases do the fourth, fifth, and sixth distances have any substantive influence.
The Allison effect is usually exacerbated by the often-recommended placement of speakers away from walls and on stands. This typical speaker siting causes the well- documented suckout of upper-bass frequencies, making cellos and basses sound thin while coincidentally seeming to enhance clarity.
Suckout is a power-response phenomenon and will influence the sound no matter where you sit. It is the result of quarter-wave cancellation effects, in which sound reflects from large nearby boundaries back to the woofer and nulls its output at certain frequencies. If the boundaries are far enough away, the suckout moves downward in frequency and begins to affect the lower bass range. A large boundary 3 feet away from a speaker will cause a power-response (not standing-wave) dip at 113 Hz every where in the room. At 4 feet, the suckout will occur at 84.75 Hz; at 5 feet the null drops to 67.8 Hz; at 6 feet it is at 56.5 Hz; at 7, 48.4 Hz; at 8, 42.4 Hz; at 9, 37.66 Hz; at 10, 33.9 Hz; and so forth.
The reason commonly given for using speaker stands is to raise the tweeter to the same height as the listener’s ears. What is important, however, is not the tweeter’s elevation relative to the listener’s ears but the quality of the sound at his ears. If a tweeter is so beamy that its height is critical, then the prime listening area must be extremely small, in which case a better solution is to tilt the speaker. Aiming the tweeter up at the listener’s head will solve the problem without compromising the smoothness of the low-frequency response.
Allison has also pointed out, by the way, that boundary augmentation/cancellation effects apply to listeners as well as to speakers. Therefore, the recommendation for keeping a speaker unevenly from the nearest three surfaces also, ideally, applies to the listener’s ears.
A single, well-designed subwoofer sit ting in a corner will ensure the most bass power input to a room, but that is not the only significant factor. The flat ness of the bass response at different points in the room depends on the free-air sub- woofer response and on the evenness of the room modes. For example, there might be a cluster of modes near one frequency within the subwoofer’s passband that could be somewhat suppressed by placing the sub away from a corner to induce a compensatory suckout. Similarly, if a subwoofer has more output from, say, 60 to 100 Hz than it does from 20 to 60 Hz, pulling it out of the corner a few feet might flatten the hump. Placing the sub close to the listener (as recommended by Hsu Research) might also have audible benefits in some cases, though this can be difficult to establish without sophisticated best "safe" bet is corner placement, at least as a starting point. Experiment by moving the sub out in increments of only a few inches, shifting its placement until the deep bass in the listening position is most satisfying.
Moving a subwoofer out of a corner reduces the output at the high end of its operating range more than at the low end because the augmentation is frequency-related. Again, that may help flatten the response with some subs, even though you’ll need more input power at the high end than you did before. It amounts to equalization by location, and a little change can make a lot of difference.
Assume a sub in a corner has its woofer 12 inches from each boundary. The augmentation is about 8 dB at 80 Hz. Moving the box so that the woofer is 48 inches away from the walls, with it still sitting on the floor, reduces the augmentation at 80 Hz to zero. So it isn’t really correct to say that a sub is acoustically “close” to all six room car (with closed windows) resembles a pressure pot over a wide range of low frequencies because of its small dimensions compared with a living room. But a living boundaries, at least not over its full range. A room approaches a pressure pot only below the lowest room-dimension resonances, which typically are in the region of 30 to 35 Hz, even for a room of modest size.
Similar to the boundary augmentation/cancellation effect, and caused by essentially the same interactions, are the spaced-speaker effects: shelving bass boost from multi-speaker coupling and a cancellation dip created by the spacing between speakers.
Allison has pointed out that at frequencies whose wavelengths are more than a quarter the distance between two speakers, there will be a shelving boost of 3 dB (assuming that the two speakers are radiating the same signal at the same level); for two speakers 8 feet apart, that would be 3 dB be low about 140 Hz. If two more speakers are added (left and right surround, for example), radiating the same signal at the same level, an additional 3-dB bass boost results. However, rarely do surround signals include the same bass, or bass at even nearly the same level, as the front channels. The exact result in a multichannel system will depend on the bass content in the various channels, the low-frequency extension of speakers, and where low frequencies are directed by the bass-management system. Consequently, results can be extremely difficult to predict.
The other side of the speaker-interaction coin is what happens at frequencies where the wavelength is smaller than that at which augmentation by mutual coupling begins. And again, the result is analogous to what happens in speaker/boundary interactions. When woofers are spaced apart, each one’s power response will have a notch whose center frequency will depend on the exact distance between the speakers. The suckout is a result of inter-woofer cancellations that are similar to what would happen if one woofer were turned off and a perfectly reflective wall were exactly centered between them. The reflections from the virtual boundary, simulated by the low-bass signals from the second woofer, would cause a dip at the same frequency. Stated another way, with two woofers the null will occur at the same frequency as a boundary effect in which the woofer-to-boundary distance is half the woofer-to-woofer distance. For example, if two woofers are 12 feet apart, or one large boundary is 6 feet from either of the woofers, a null will occur at 56.5 Hz.
The dip will not be very significant sonically unless it is reinforced by a second, boundary-generated dip at the same frequency (note again that this is not about position-independent standing-wave effects). If both speaker-spacing and boundary cancellation occur at the same frequency, the dip will be deeper and more audible. To minimize the adverse effect of using two woofers in the low-bass range, it is important to make sure that they do not also interact with boundaries that are half the distance from either woofer as the two woofers are from each other.
Two woofers placed in two corners would have only one cancellation dip, which would probably not be deep enough or broad enough to be audibly significant with musical program material. Under most conditions, the flattest bass is radiated into the room by placing a single woofer in a corner, the biggest advantage of which is the uniform reinforcement from three adjacent surface boundaries—something that two subwoofers placed in two corners the various speakers, the placement of those would also have although they would still have that cancellation null at one frequency because of their spacing. For example, two woofers in corners 20 feet apart would have a dip at about 34 Hz. However, other room effects (the cancellation effects caused by boundaries plus, of course, standing waves) would cause similar aberrations.
Interestingly, if two main-channel satellite speakers are placed 6 feet apart, the inter-woofer null will occur at 113 Hz, meaning that a single subwoofer in a corner, crossed over at 80 Hz, will not eliminate the suckout. Indeed, with 8-foot spacing, the resulting 85-Hz suckout might foul up the 80-Hz crossover blend between the sub- woofer and the satellites. As noted above, however, this becomes a serious problem only if the speakers are the same distance from a wall as half the distance between the speakers.
STANDING WAVES VS. BOUNDARY INTERACTION
Suckouts—the wave-cancellation nulls caused by interaction between two speakers or between a speaker and a boundary—are not the same as standing waves. Standing waves are determined solely by boundary-to-boundary distances and occur independent of where acoustic power originates in the room; that is, they are purely acoustical effects, not power response effects. Suckouts, whether caused by speaker-to-boundary or speaker-to-speaker cancellations, are power-response nulls.
Standing waves control the distribution of power, not the amount; they are fixed spatially in the room, the pattern varying with the frequencies involved. They cause the bass balance of a program to change dramatically as a listener move around a room. Suckouts affect power response and cannot be changed by moving the listener although moving him/her will change his/her relationship to standing in ways that may ameliorate or exacerbate the subjective effect of a suckout.
To change a suckout frequency, move the speakers in relation to each other or to boundaries. Optimally, moving two woofers next to each other and into a corner eliminates the null completely, ii the crossover point is below the frequency where the three close boundaries in the corner would cause a null in the upper bass.
Adapted fom: Audio magazine, July/Aug. 1999
Also see: Coloration of Room Sound by Reflections (Mar. 1993)
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