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Room Acoustics Part 2

Room Acoustics

This is the second part of the Room Acoustics article.

C3 - Reverberation distance
C4 - Rooms for multi-channel sound
C5 - Amplifier power to obtain Reference Level
C6 - Room response time

D - Loudspeaker and listener placement

C3 - Reverberation distance

When we consider radiation in the reverberant frequency range above 149 Hz, the sound at the listening position is composed of the direct sound from the source and the reverberant sound that is more or less uniformly distributed in the room. The direct sound pressure level decreases inversely to distance from the source and will equal the reverberant sound pressure at distance xr. The ‘reverberation distance’ xr (also called 'critical distance') is calculated from

xr = 0.1 ( G V / (p T60) )1/2 [m] (10)

where the directionality gain G is unity for a monopole and G = 3 for a dipole radiator. A dipole, thus, has a 31/2 = 1.73 times larger reverberation distance.


A typical reverberation distance is actually quite small, 0.72 m (2.4 ft) for the monopole and 1.24 m (4.1 ft) for the dipole in the example room. Never-the-less, the ratio of direct sound Ld to reverberant sound pressure level Lr is 4.8 dB greater for the dipole than for a monopole with the same direct sound output. Thus, at 3 m distance from the source, the direct sound would be 20*log(3/0.72) = 12.4 dB below the reverberant sound field for the monopole and only 20*log(3/1.24) = 7.7 dB below it for the dipole.

The 4.8 dB lower level of the reverberant field in the case of the dipole significantly reduces the masking influence of the room upon sonic detail. It eliminates the sensation of overload of the room during loud passages of program material and makes your listening sessions much less noisy to your neighbors.
You have often experienced the poor intelligibility of spoken words from PA systems in enclosed public spaces. Usually a central cluster of loudspeakers aims at the audience. In reality the speakers are not very directional and too much sound is radiated towards useless spaces, only to bounce around and raise the reverberant sound level. It does not help to increase the volume to obtain more direct sound, because it also raises the reverberant sound level. Speech modulation gets lost in this, somewhat like the loss of articulation in my woofer test signal.

C4 - Rooms for multi-channel sound

It has been suggested (R. Walker, BBC, 1998) that the reverberation time T60 over the 200 Hz to 4 kHz frequency range be adjusted to

T60 = 0.3 (V/V0)1/3 [s] where V0 = 100 m3 (11)

with a tolerance of +/-50 ms which is allowed to increase linearly to +300 ms between 200 Hz and 63 Hz.
The room of Example 2 should thus have T60 = 300 ms +/-50 ms. This makes for a subjectively quite dead room, which is fine if the room is dedicated solely to Home Theater and surround sound, but is in my opinion a very overstuffed environment for normal living. It has the effect of making the reverberation distance xr = 1.04 m for the monopole and xr = 1.8 m for the dipole. At a viewing/listening distance of 2 m the direct sound is only about 6 dB below the reverberant level of the monopole which is good for sound clarity.
Instead, you could use a dipole, increase T60 to a much more livable 600 ms and have the same direct-to-reverberant ratio as for the monopole for which the specification was developed.

C5 - Amplifier power to obtain Reference Level

When you know the equivalent sensitivity Ls of your speaker in dB SPL at 1 W (2.83 V across 8 ohm) and 1 m distance and the reverberation time T60 of your room, then you can estimate the amount of power Pref required to obtain a specified reference level Lref at the listening distance xl. First calculate the reverberation distance xr from (10). Then the level of the reverberant field for 1 W into the speaker is

Lr(1W) = Ls - 20 log(xr) [dB SPL] (12)

If the listening distance xl is greater than xr, then the amplifier power in dBW is

Pref = Lref - {Ls - 20 log(xr)} [dBW] for xl > xr (13)

Example 3
Ls = 89 dB SPL at 1 W, 1 m
Lref = 85 dB SPL

xr = 1.04 m for T60 = 300 ms
Lr(1W) = 89 - 20 log(1.04) = 88.7 dB SPL
Pref = 85 - 88.7 = -3.7 dBW, equivalent to 10(-3.7/10) = 0.4 W

xr = 1.8 m for T60 = 300 ms
Lr(1W) = 89 - 20 log(1.8) = 83.9 dB SPL
Pref = 85 - 83.9 = 1.1 dBW, equivalent to 10(1.1/10) = 1.3 W

With a suggested 20 dB of SPL headroom over reference level the monopole requires 40 W and the dipole 130 W to set up a 105 dB SPL reverberant sound field. The dipole's direct sound, though, is 4.8 dB higher than the monopole's and will be 105 - 20 log(3/1.8) = 100.6 dB SPL at 3 m distance. The increased clarity could be traded off for a more lively room with larger T60 and the same 40 W amplifier power and direct-to-reverberant SPL ratio as for the monopole.

C6 - Room response time

It takes time to build up the reverberant sound field in a room. Combining the expressions for rise time (2) and T60 (3) we obtain

Trise = 0.32 T60 [s] (14)

You can think of Trise as the time constant of the room. If music or speech varies faster than the time constant, then the room will not respond fully and you hear predominantly the direct sound from the speaker. For 630 ms reverberation time and 200 ms rise time this covers modulation envelopes of a sound down to 1/200ms = 5 Hz which, in my opinion, is preferable over the 10 Hz envelope rate of a T60 = 300 ms room.

In all practical cases the room response time is large compared to the time it takes a reflected sound to reach the listener and therefore reflections will not be masked by the reverberant field. Depending upon the directivity of the source and the proximity of reflecting surfaces and objects specific absorptive or diffusive treatment may become necessary. It should not be overdone, though, because a certain amount of lateral reflection is subjectively desirable to not destroy the impression of a real space.

D - Loudspeaker and listener placement

It is often assumed that a study of room acoustics can lead to highly specific loudspeaker and listener placement locations, down to within an inch. Other proponents are not as optimistic and recommend a 1/3rd rule (FAQ31). I have come to the conclusion that real rooms are acoustically far too complex to predict the transmission of sound from speaker to listener, where the sound paths are in three dimensions, have direction and frequency dependent attenuation and diffusion, and can excite the inherent resonance modes of a room to unknown degrees.

From practical experience I recommend the following setups as starting points. They are for ORION, a dipole or bi-directional loudspeaker, and for PLUTO, a monopole or omni-directional speaker. Three room sizes are considered. The 180 ft2 (17 m2) room with 8 ft (2.4 m) ceiling would seem like the absolute minimum for quality sound reproduction with the ORION. A 400 ft2 (37 m2) or larger room with 10' (3 m) ceiling should be perfect.

D1 - Dipole setup


ORION separation is 8'. They are slightly towed in. The listener is at the apex of an equilateral triangle. Distance to the wall behind the speakers is 4', and to the side walls 2'.
The listener is only 4' from the wall behind, and this might require some heavy curtains and other absorbing material on that wall. As the room gets larger it expands around this triangular setup and especially behind the listener. Sound should just wash by the listener and disappear.

The wall behind the speakers should be diffusive. The rear radiation from a dipole must not be absorbed or it is no longer a dipole. Similarly, the side walls should not absorb sound at the reflection points but diffuse it. A dipole can even be towed in so that the listener sees the radiation null axis in a wall reflection mirror.

D2 - Monopole setup


PLUTO setup differs from ORION. The listener sits closer to the speakers. The distance to the wall behind the speakers can be slightly less, because of the uniform acoustic illumination of the room. It should not be less than 3' (<6 ms) to separate reflection from direct sound psychoacoustically, and to preserve phantom imaging.
Sidewall reflections should be diffused if treated at all. Absorbing them is like turning down the tweeter. Absorbers are not broadband and ineffective below a few hundred Hz.. Besides, lateral reflections are important for sound scene recognition.

Again, larger rooms expand around the triangle and increase the space more behind the listener than in front of him.

D3 - Pink noise test

Listening to pink noise is a revealing test of electrical and acoustic performance of any system setup. Pink noise must emanate from both speakers simultaneously in dual mono fashion. A tightly confined phantom image should be heard half-way between the two loudspeakers. As you move your head left or right the sound should become brighter sounding and increasingly so with about a 2 inch (5 cm) periodicity as the lateral head displacement is increased in D1. The image also becomes significantly more diffuse and moves towards the nearest speaker. Pink noise should sound neutral and uncolored, though what that exactly means is hard to define. Moving around in the room the character of the noise sound should not change significantly with speakers like ORION and PLUTO, holding up even when you leave the room and listen from outside. This is not the case with loudspeakers that have a greatly varying polar response.

Listening to pink noise does not give a reliable indication of system performance at frequencies below 100 Hz and above 10 kHz. Even when pink noise is measured in 1/3rd-octave bands, the response graph is not a reliable indicator of speaker performance and should not be used as the basis for equalization. It seems so obvious that one only needs to have a flat frequency response at the listening position and be done. But, room response equalization is a very complex subject because it deals with sound in three dimensions of space, with time, with frequency, and with a highly evolved auditory stimulus processor between the two ears that is not easily fooled long-term. The response should not be optimized merely at the listening position. Few commercial products deal with this adequately.

D4 - Room analysis

The modes 1.xls spreadsheet that was discussed under C above can be used to analyze the three hypothetical rooms and to gain some general insights. Depending upon their structural rigidity, their wall surface textures, floors, floor coverings and objects in different locations, each room will have its own unique acoustic signature. Broadly speaking, a room may sound live or dead. The extremes of this would be an unfurnished room with hard walls versus a cocktail lounge full of overstuffed armchairs and soft leather. Neither one would be suited for sound reproduction. The descriptive parameter is the average absorption coefficient of all surfaces and leakage paths. By definition an open window has a 100% absorption coefficient and if that open window covered 20% of a room's total surface area, then the average absorption coefficient for the room would be 20%. For the 180 ft2 room example this would be an open window of 169 ft2 area out of a total surface of 847 ft2. Since we usually listen with closed windows and very few surfaces have 100% absorption, it takes much more than 169 ft2 to obtain an overall 20% absorption.

room acoustics table 1

The numbers in tables D5 and D6 are for hypothetical rooms and based on a very simple rigid rectangular room model. Though the numbers look precise they should only be taken as trend indicators. Note the relatively narrow range from 99 Hz to 200 Hz covered by the Schroeder frequency for the different rooms and absorptions. Below this frequency specific room modes can dominate, down to the 1st mode. Above that frequency the mode density becomes so high that a room is better described statistically by its reverberation time. For the typical home listening rooms with relatively large objects and different materials in them, reverberation time usually changes with frequency regions and is not as solid a descriptor as for concert halls. Below the first room mode the sound level becomes independent of location in the room and is a function of the lumped mechanical properties of the room. Similar to the modal region the level can be attenuated or amplified depending on wall surface flexures and leaky openings. The room adds to and subtracts from the loudspeaker's direct sound to varying degrees and in a very complex manner over the whole frequency range of the speaker. Thus the tables can only show trends above the Schroeder frequency.

It can be seen in D5 that the reverberant SPL in the 400 ft2 room is 3.1 dB below that of the 180 ft2 room and when the absorption is increased to 40% in D6, it drops by another 3 dB for the same direct sound level. Since we judge loudness by the reverberant sound field this means that the volume control setting has to be increased 3.1 dB for the volume in the 400 ft2 room to be as loud as in the 180 ft2 room in D5, and by 6.1 dB for the more absorptive room in D6. Still, this is not much of an increase between the small and the large room. It confirms that ORION and PLUTO can be used in a wide range of room sizes, if volume levels are set for critical listening in the triangle seat and not for sound reinforcement at a large party.

Under D6 the ratio of direct to reverberant sound level is 3 dB better than for the more lively rooms under D5 with half the absorption. These numbers are for the dipole which inherently is 4.8 dB (3x) better than a monopole. But the monopole in D2 is closer to the listener than the dipole in D1. Thus, in all cases the direct-to-reverberant sound ratio for this monopole at 6.4' (1.92 m) listening distance is only 2.8 dB worse than that for the dipole at 8' (2.4 m).

Despite the poorer signal-to-reverberant ratio I find more lively rooms preferable for music and voice reproduction. Home Theater installers, though, try to get rooms down to the 200 ms T60 region, which is difficult to accomplish for low frequencies.

Reverberation time of a listening room can be measured rather easily with the NTI Acoustilizer, but a loud hand clap can tell already whether a room is live or dead. Rather than special products for acoustic treatment of a room I prefer the normal stuff of life - books, curtains, pictures, rugs, wall hangings, shelves, cabinets, chairs, sofas, etc. - to establish the acoustics of my living spaces. ORION and PLUTO+ are well adapted to such spaces which also convey a friendly atmosphere to most people.

Article written by Siegfried Linkwitz

Source Linkwitzlab

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