Room acoustics (long)

General Asylum

General audio topics that don't fit into specific categories.

212.206.88.5

The following is as complete as the papers referenced to allow to be. Some points certainly would require more detailed evaluation, but I think it's a helpful starting point for those interested.
**************************************************************
An octave is the frequency range between a first frequency f and a second frequency 2f.
**************************************************************
Distinction has been made between the frequency range of 0-300 Hz and above 300 Hz [1]. The reason is that in terms of wavelength of sound, listening rooms are acoustically small for lows and acoustically large for highs. A further reason is that below 300 Hz the room dominates the loudspeakers'
behaviour [8, 9]. The formula for the average density of room modes (number of modes per hertz of bandwidth) shows a dependence of the room's volume and the square of the frequency [20]. In larger rooms the density is greater than in smaller rooms. Above 300 Hz, sound colouration phenomena
disappear [20].

In the low frequency range, 3 types of resonance modes exist : the dominating axial mode, and the less important tangential (3 dB down) and oblique (6 dB down) modes. Tangential and oblique modes can not be ignored simply because of their low energy level as compared to the axial modes [12]. Axial modes involves reflections from two surfaces, tangential modes
from 4 surfaces, oblique modes from 6 surfaces. Axial modes are made up of TWO travelling waves propagated parallel to one axis, tangential modes of FOUR travelling waves and oblique modes of EIGHT travelling waves. So the reduction of energy per wave for tangential and oblique modes 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. A calculated room resonance series based on only on axial standing waves is incomplete and will lead to erroneous conclusions [12].
Axial modes have harmonics and secondary modes [9]. Tangential and oblique modes are of higher frequencies than the lowest axial mode [9].
Tangential or oblique modes of high initial intensity or wide spacings (with respect to other frequencies) may possibly be audible [7]. Spacings of more than 20 Hz should be avoided, with clustering near certain frequency being even less desirable because of the creation of a peak at
that frequency. For minimal colouration, modes should be spaced in order to avoid clustering in some parts of the frequency spectrum and their absence in others [20].
In the frequency region of interest, the response is characterized by large peaks at mode frequencies with significant dips between. The total range of
response levels is about 20 dB [21].
At or near the mode frequencies, sound pressure will be enhanced. Above an upper limit (Schroeder frequency, see below), there will be very many modes present and this amplification affects all the sound, providing a smooth
response. At frequencies below that limit and between the modes, the enhancement will not occur. This will be perceived as relative attenuation, creating an irregular response [22].
When room dimensions are the same (worst case : cube) or exact multiples of each other, modes can cluster at certain frequencies, creating room boom [9]. Up to mode (2, 2, 2) there are 26 modes in a room [13]. In a 20 foot cube there are 7 frequencies at which multiple modes exist : 29, 40, 57,
64, 70, 81, 86 Hz. At 64 Hz, six modes combine to produce a very large resonant peak [13].
Resonance = standing waves, which are determined purely by the dimensions of the room, or, more precisely, by the distances between existing rigid reflection surfaces (furniture does count, also the speakers when positioned such that their side surfaces are parallel). The more rigid are the reflecting surfaces, the better the standing waves are maintained [12].
Doors and windows cause a greater bass loss from the room than the walls [12]. Open windows work like perfect absorbers.
The frequency is calculated by [1,12]
f = 1,130 ft/sec / 2x distance between surfaces.
or by [8, 20]
f = c/2 x sqrt [ a2 + b2 + c2]

with a = nx/Lx
b = ny/Ly
c = nz/Lz
nx, ny, nz integers with chosen values between 0 and 4
Lx, Ly, Lz length, width, height
c = speed of sound (345 m/s)
Axial modes :
(1, 0, 0), (0, 1, 0) , (0, 0, 1) : 1st order mode
(2, 0, 0), (0, 2, 0) , (0, 0, 2) : 2nd order mode
(3, 0, 0), (0, 3, 0) , (0, 0, 3) : 3rd order mode
Tangential modes :
(1, 1, 0), (0, 1, 1) , (1, 0, 1)
(2, 2, 0), (0, 2, 2) , (2, 0, 2)
Oblique modes : all possible combinations of three integers

Room mode distribution [17]:
N = df ( 4piVf2/c3 + piSf/2c2 + L/8c)
N = number of normal modes in a frequency band
df = frequency bandwidth centred on f
c = velocity of sound
V = room volume
S = total surface area of walls
L = sum of all room lengths
The analysis shows that the number of modes per 1/3 octave band is small and increases exponentially with frequency. At some frequency the room modes become so close that a uniform response (= essentially flat frequency response [19]) can be expected.
The frequency of uniformity is given by [17]
f = sqrt (c3/4piVdf)
A 15 feet wide room has a resonance frequency in the axial mode of 37.7 Hz [1]. The harmonics of that frequency, i.e. 75.4 Hz, 113.1 Hz, 150.8 Hz etc. will also be resonance frequencies between those surfaces. One calculates
those frequencies for width, length and height of the room to obtain a list of resonance frequencies. Furniture adds reflecting surfaces that have to be taken into account [4].
A room connected to the listening room by a common opening (door etc.) adds its resonance frequencies to the ones of the actual listening room [10].
Each frequency has in a normal room a bandwidth of about 5 Hz [1], meaning that in a room with resonance at 50 and 53 Hz a strong signal at 50 Hz excites the 50 Hz mode and also forces the 53 Hz mode to vibrate at 50 Hz.
When the exciting component of the signal is removed, both modes decay at their frequencies of 50 and 53 Hz, returning energy into the room. The 53 Hz energy which was not present in the original signal causes colouration of sound.
The bandwidth of a room mode is calculated as follows :
df = 6.91/piT60
and is for small rooms between 3 and 10 Hz [20].
Note that calculations are based on ideal conditions, i.e. perfectly rectangular, flat and rigid reflecting surfaces. Reality is different so that errors in the calculated frequencies may occur [8].

Room dimensions:
A listening room should be dimensioned such that there is no clustering near certain frequencies and such that excessive gaps between adjacent frequencies are avoided.
Ratios of height, width and length that are acceptable are 2:3:5, 1:1.6:2.5, 1.236:2:3.236 (Golden rule ratio) [4].
A most highly recommended room dimension ratio is 1:1.4:1.9 [12].
However, when one enters an empty room or places a chair in it one changes the ration of room dimensions from an acoustic point of view.
Suggested ratios are based on third-octaves, 2 n/3 [13], where n is any integer not divisible by 3 (e.g. 0, 1, 2, 4, 5, 7 etc).
For optimum room dimensions the following conditions should be met [20] :
1. The curve spectral density of modes vs frequency (see formula for room mode distribution above) should increase monotonically. Each one-third octave should have more modes than the preceding one.
2. There should be no double modes. At most, double modes only in one-third-octave bands with densities equal to or greater than 5.
Another dimension ratio is proposed by Walker [21] :
Based on the concept of mean-square room quality index (the frequency differences between every pair of modes is squared and summed, the total being divided by the number of modes included) the following criterion is proposed :
1.1 w/h l/h 4.5 w/h-4 (l, w, h = length, width, height)
Room volume:
A larger room will yield a better bass response than a smaller one. An exception from this is a very small volume [12].
At frequencies below the lowest axial mode, the very small room acts as a pressure chamber, the entire space being pressurized by the woofer, resulting in a reinforcement of those frequencies (12dB per octave). The smaller the room, the higher the lowest axial mode : the smaller the room, the easier it is to get deep bass [9].
At frequencies below the lowest axial mode (determined by the room's length) the motion of the woofer membrane excites the room as though it were principally a compliance [13]. The pressure in the room increases as the frequency gets lower for a constant volume velocity (motion) from the woofer. It is this pressure, which is mainly uniform throughout the room,
which the ear hears. The statement that below the lowest axial room mode no frequencies can be transmitted by the woofer because the waves don't fit in the room, is therefore not true [13].
The main advantage of the large room is that the Schroeder frequency is lower than in a smaller room. The Schroeder frequency is the frequency above which the standing waves are so closely spaced that they do not substantially affect the sound [12, 13]. It is dependent on room volume and
reverberation time. The larger the room or the shorter the reverberation time, the lower that frequency. A low Schroeder frequency tends to make the frequency response smooth over a wider range [12].
The Schroeder frequency marks the transition from individual, well separated resonances to many overlapping normal modes [18]. It is calculated as follows :
fc = 2000 sqrt T/V
T = 60 dB reverberation time in seconds
V = Room volume in m3
which has a a consequence that at least three resonances fall within the half-power bandwidth B (B = 2.2/T) of one resonance at frequencies above fc.
Colouration of sound depends on [1]
1. bandwidth of modes
2. degree of excitation
3. separation of modes from strongly excited neighbours
4. frequency content of the source
5. position of speakers and listener
The pressure distribution of modes is such that maximum for axial modes is at the reflecting surfaces. A first order axial mode has one null (or minimum) line in the middle between the two surfaces. A second order axial mode (first order harmonic) has two null (or minimum) lines between the surfaces etc. Tangential and oblique modes have pressure maxima in the
room's corners. ALL modes terminate in corners. The resonance effect occurs no matter where the speaker is placed with respect to the surfaces [12].
Room treatment [1]

1.calculate the axial modes (includes harmonics) for the listening room (up to about 300 Hz)
2.try to identify by listening at which frequency distortion occurs, choose music rich in lows or speech
3. identify the mode corresponding to that frequency
4. place an absorber effective at that frequency at the place where the corresponding mode has a maximum.
5. to simplify, choose the "overkill" solution by placing wideband absorbers in all corners (or other adequate locations), thereby reducing magnitude of all modes.
Non-rigid surfaces tend to vibrate, absorbing sound energy. In such case, "overkill" or extensive absorber placement may deaden the room's ambience.
Thin pliant walls are better than rigid concrete ones. Resilient wall mounting is sonically better than those that use mass alone [9]. Bass traps for frequencies below 100 Hz are large and have to be used only after detailed measurements.
Loudspeakers are nondirectional at low frequencies, so that a change in the speakers' orientation does not provide a solution to avoid extensive bass.
Nearby reflecting surfaces may enhance lows output by some 6 to 12 dB, making equalization necessary (unless one likes plenty of bass). However, equalization is merely decreasing some modal peaks.

Good placement of speakers and listening seat is the best and easiest remedy. Subwoofers need to be in high-pressure regions, against the wall or in the corners [8]. The listening seat should be in a null in the room's mode pattern for too much energy at a room mode. Too little energy means
moving the seat towards a peak. Toole offers a PC program for establishing the room mode pattern of listening rooms [8]. Establish a room mode pattern using the second formula given above (or the mentioned program) and chose places for speakers and seat according to that pattern.
If the room is not rectangular or if there are large openings, calculations will not work well. Measurements should then be made. Non-rectangular rooms do not eliminate room resonances, they just make it more difficult to calculate [8, 9].

Room treatment [10]
If room dimensions are such that they are multiples of each other, change length or width (by adding furniture covering the corresponding wall from ground to ceiling : 10.000 LPs cover a surface of about 4x5 m ) to change that relationship. A large opening towards a neighbouring room may help.
Install non-rigid double walls for the wall causing a predominant resonance.
Room treatment [19]
Absorbing material has to be applied to
- short walls for the (1, 0, 0) axial mode
- either a long or a short wall for tangential modes
- any surface for oblique modes
Sound absorbers are essentially of three types : dissipative (fibrous or porous), panel (vibration) and cavity (Hemholtz).
1. Dissipative absorbers cover a rather wide frequency range, the absorption coefficient increasing with frequency.
They have to be placed such that the face of the material is at about one quarter wavelength from the wall. Therefore, they have to be either very deep of spaced significantly from the wall. They are of greater effect at lower frequencies because the effective distance is greater than the actual distance when the sound wave arrives at angles different from 90 degrees.
Fabrics to cover the actual absorbing material for reasons of aesthetics may reflect waves (at higher frequencies) rather than be acoustically transparent.
Suspended fabric can serve as reasonably effective upper frequency absorber. It must be spaced from the wall and sufficiently dense to provide resistance to the motion of the air particles. The weight determines an inherent low-frequency cutoff. Below this frequency, the fabric will merely move back and forth without absorption effect.
2. Panel absorbers
Two types : stretched membrane in which the frequency peak is dependent on mass and tautness of the membrane; panel absorbers, where the peak is determined by mass and bending stiffness of the panel.
3. Cavity absorbers (Helmholtz resonator)
Effectiveness depends on hole diameter, hole length and volume of the chamber behind the hole.

Absorbers of type 2 and 3 cover only a narrow frequency band centred on the peak frequency.
A combination of dissipative and resonant absorbers may result in less absorption over a broader frequency range due to damping of the resonant absorber.

Room treatment [22]
Arranging acoustic absorption elements increases the damping factors of the modes, thus reducing maximum amplitude of the modes enlarging the bandwidth. This results in reduced mode spacing and decreases the frequency where the modes are to be considered to be overlapping. Such a room, however, would sound lifeless.
All modes have pressure maxima at the reflection surfaces (walls). Placing the speaker there ensures that it is better coupled to more of the room modes, which helps to reduce response irregularities. Such location would, however, affect the sound image or spatiality. Use of a subwoofer could
avoid such problem.
Diffusion of standing waves [19]:
Regularizes the frequency spacing. If the dimensions of the room are great in comparison with the lowest frequency (wavelength = velocity/frequency) to be generated, diffusion becomes less important because the lowest order standing waves are at higher frequencies and thus more or less closely
spaced (uniformity, Schroeder frequency).
The diffusing surface irregularity (e.g. saw-tooth shape) should be of a dimension greater than a half wavelength at the lowest frequency to be dealt with.
Standing waves are of importance not only because of their own contribution to a room's response but also because reverberation time, frequency response and diffusion of a room are almost solely dependent on the number, distribution and degree of damping of standing waves [19]. Damping of standing waves by absorption results in a flat response for higher
frequencies due to better absorption characteristics at these frequencies.
Damping the narrow peak of a standing wave results in a peak of lower amplitude but of greater width [19]. The gaps between standing waves at higher frequencies, which are closer spaced than at lower frequencies, are filled into a more continuous spectrum. The amplitudes are hence reduced and their spectrum is broadened as to result in a more flat response.

Reflections [2] :
Sound is made up of three components :
1. direct sound
2. first reflections
3. multiple reflections (reverberation)
Reflected sound arriving immediately after the signal is masked as far as localization is concerned, but it does affect sound quality. Reflections are weaker than the signal because of greater distance travelled and losses at reflecting surfaces. Single bounce reflections are rarely more than 10
dB down from the direct signal and therefore dominant (as compared to multiple reflections). Lateral reflections at levels of as much as 30 dB down from the direct signal can still be perceived [15].
Multiple reflections and reflections from the rear of the room are delayed more than the first reflections but they are of less immediate significance because their level is low due to the greater distance travelled and to multiple reflection losses [2].
It has been observed [6] that reflections affect directional and spatial impression rather than timbre or sound colouration.
The direction from which the reflection arrives has no influence on its effectiveness [6]. Exception : when the reflection comes from the same direction as the direct signal, masking occurs (5-10 dB) [2, 6]. Importance of first reflections in decreasing order [1]: floor (1 dB down), ceiling (1.5 dB down), walls (1.5-5dB down), rear wall (5.5 dB down), reverberations (which are late reflections that tend to be merged) (6 dB and more down). {Values are from a graph without scale and related to the level of the direct sound}.
Audibility of reflections [2, 6]:
The observer is seated in an anechoic room facing one speaker radiating the direct sound and a second speaker radiating the simulated reflections.
Level and delay of the reflection can be adjusted.
At a certain delay setting the level of the reflections is increased until something different is heard (1st threshold). A sense of spaciousness is perceived, making the anechoic room sound like a normal room. Further level increase increases the spatial effect. A 2nd threshold is found: now the image broadens and shifts away from the direct source. Upon further level increase a 3rd threshold is found : the direct sound is now perceived along with a discrete echo.
Repeating the above procedure for various delay times and reflection levels results in a graph presenting 3 lines corresponding to the 3 thresholds.
Reflections having levels and delay values which place them in the area below the lowest curve are not heard at all. Reflections having levels and delay values which place them in the area above the upper curve are perceived a s echos and as such detrimental to the primary sound.
Sound reflected by surfaces loses highs because of the absorption characteristic of he surface, meaning that the reflected sound has a different spectrum than the sound from the source, thus affecting timbre.
Some absoption coefficients for 125 Hz (for 4000 Hz between brackets) concrete 0.01 (0.02), marble or glazed tiles 0.01 (0.02), carpet or linoleum on concrete 0.02 (0.65), brick 0.03 (0.07), fabric in contact with wall 0.03 (0.35), wood parquet on concrete 0.04 (0.07) , wood 0.15 (0.07), large glass panes 0.18 (0.02), plywood panel 0.28 (0.11), window 0.35 (0.04).
Some absorption values for furniture [10] : these values can be added as such to the total absorption characteristic A of the room.
sofa : 0.70
2 armchairs : 1.40
table : 0.50
2 cupboards : 0.60

Room treatment [2]:

Floor reflections : place a mirror on the floor such that both tweeters can be seen (from usual listening place). A thick rug should cover both spots.
Ceiling reflections : use the mirror technique, cover with acoustic tile, glass fibre, acoustic foam etc.
Rear wall : locate shadow image on the wall, place carpeting or drapery going about 1 foot beyond shadow boundaries.
Side walls : use mirror technique to determine reflection spots. Place absorbing material until desired effect is achieved.
Wall behind listener : place absorption elements to reduce reflection intensity and to reflection peaks spread them over time [15]
Too much absorbent material may result in the room being too dead.
The absorption coefficients given above multiplied with the corresponding surface(s) results in the absorption characteristic A of the room. The reverberation time T60 is arbitrarily defined as the time required for a steady-state sound energy density in a room to decrease, after the source
is stopped, to one millionth of its original value, or 60 dB [11]. It is calculated using a formula by Sabine : T60 = 0,16 x V/A (V=volume of room, all length units in m) and should be between 0,2 and 1 second for domestic rooms [10]. The original Sabine formula, however, is T60 = 0.049 x V/A [19].
Reverberation is present for a frequency range where the wave length is inferior to the room dimensions, i.e. about 300-3000 Hz [10].
IEC 268-13 (Sound system equipment : listening tests on loudspeakers) requires a reverberation time of 0.4 Â± 0.05 s for the frequency range of 250 to 4000 Hz, and it should not exceed 0.8 s for frequencies below 250 Hz. A less stringent criterion given is that the average value shall be within 0.3 to 0.6 s, with a maximum deviation from the average of 25 % for individual values [16].
Diffusion of reflections :
The important point regarding sound diffusion is that is does not lessen the total energy in the room, but rather it increases the number of reflections per time unit and hence lessens the intensity level of the individual reflections [14].

Flutter echoes [19]
Repetitive echo fluttering back and forth between two parallel surfaces.
Unlike echoes, they can occur in rooms of any size. In smaller rooms it will sound like a buzzing or ringing. Treating an offending wall with absorptive material will help.
[1]Everest, The uneasy truce between music and the room, Audio, Febr.1993,p.36
[2]Everest, Colouration of room sound by reflections, Audio, March 1993,p.30
[3]Allison, The influence of room boundaries on loudspeaker output, JAES 1974, p.314
[4]Rettinger, Small music rooms, Audio Oct.1968, p.25
[5]Griesienger, Spaciousness and localization in listening rooms and their effects on the recording technique, JAES 1986, p.255
[6]Olive, The detection of reflections in typical rooms, JAES 1989, p.539
[7]Gilford, The acoustic design of talks studios and listening rooms, JAES 1979, p.17
[8] Toole : Maximizing loudspeaker performance in rooms, Loudspeaker and rooms - working together (white papers at >www.harman.com<)
[9] Nousaine : Room acoustics at low frequencies, Audio 1998, June, p.32
[10] Goldenberg : L'amenagement du lieu d'ecoute, Haute Fidelite, 4/5 2000, p.36
[11] Everest : The acoustic treatment of three small studios, JAES 1968, p.307
[12] Weinberg : Bass vs space, Audio 1999, July, p.28
[13 Sehring : Taking up resonances, Audio 1993, April, p.32 ; addendum : 1993, May, p.12 ; 1993, June, p.8, 11
[14] Volkmann : Polycylindrical diffusors on room acoustic design, JASA 1942. vol.13, p.324
[15] Wrightson : Psychoacoustic considerations in the design of studio control rooms, JAES 1986, p.789
[16] Bech : Perception of timbre of reproduced sound in small rooms : influence of room and loudspeaker position, JAES 1994, p.999
[17] Groh : High-fidelity sound system equalization by analysis of standing waves, JAES 1974, p.795
[18] Schroeder : The "Schroeder frequency " revisited, JASA 1996, vol.99, p.3240
[19] Farrell : Room acoustics of studios, JAES 1972, p.34
[20] Bonello : A new criterion for the distribution of normal room modes, JAES 1981, p.597
[21] Walker : Optimum dimension ratios for small rooms, 100th AES convention 1996, preprint no.4191
[22] Walker : Room modes and low frequency response in small enclosures, 100th AES convention, preprint no.4194
**************************************************************
The fact that the engineering science of room acoustics exists does not imply that a particular domestic listening room does sound bad or unpleasant. Room acoustical treatment is more often applied to recording studios and concert halls than to domestic rooms.
Strategic placement of speakers (subwoofers) and listening seat can help a lot and does not involve any costs. For thorough and efficient treatment measurements are the only way, though (no physician can cure without diagnosis).

Happy reading

Klaus

This post is made possible by the generous support of people like you and our sponsors:

Schiit Audio

Topic - Room acoustics (long) - Klaus 07:01:35 08/11/00 (7)

Some Comments on the Treatment Recommendations - Jon Risch 20:21:39 08/11/00 (1)

Re: Thanks for your comments - Klaus 00:50:17 08/14/00 (0)

Reflection picture - Werner 07:22:24 08/11/00 (4)

Re: Reflection picture - Rob Doorack 20:56:28 08/11/00 (0)

Re: Reflection picture - Frank Habrle 11:46:32 08/11/00 (2)

Re: Reflection picture - Werner 03:48:08 08/12/00 (1)

Go back and read your own post! - Frank Habrle 22:26:04 08/12/00 (0)

You can not post to an archived thread.