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Chapter 9. Diffusion

Kwang Soo Cho

on 29 October 2012

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Transcript of Acoustics

Acoustics Chapter 9. Diffusion Index

The Perfectly Diffuse Sound
Evaluating Diffusion in a Room
Steady-State Measurements
Decay Beats
Exponential Decay
Spatial Uniformity of Reverberation Time
Absorbent in Patches
Concave Surfaces
Convex Surfaces : The Polycylindrical Diffuser
Plane Surfaces 눈의구조 Randall and Ward have suggested the following :
• The frequency and spatial irregularities obtained from steady-state
measurements must be negligible.
• Beats in the decay characteristic must be negligible.
• Decays must be perfectly exponential (they will appear as straight lines on a
logarithmic scale).
• Reverberation time will be the same at all positions in the room.
• The character of the decay will be essentially the same for all frequencies.
• The character of the decay will be independent of the directional characteristics
of the measuring microphone. The acoustical response of playback systems in rooms are never as flat as the response of electrical devices.
These deviations are partly due to nondiffusive conditions in the room.

Diffusion is welcome because it helps envelop the listener in the sound field. On the other hand, too much diffusion can make it difficult to localize the sound source. Evaluating Diffusion in a Room The Perfectly Diffuse Sound Field Steady-State Measurements A slowly swept sine-wave sound-transmission response of a 12,000-ft3 studio.
Fluctuations of this magnitude, which characterize many studios, are evidence of nondiffusive conditions. Decay Beats We can compare the smoothness of the reverberation decay for the eight octaves from 63 Hz to 8 kHz. In general, the smoothness of the decay increases as frequency is increased.

Beats in the decay are greatest at 63 and 125 Hz. If all decays have the same character at all frequencies and that character is smooth decay, complete diffusion prevails. In practice, decays with significant changes in character are more common, especially for the 63-Hz and 125-Hz decays. Exponential Decay Exponential Decay A truly exponential decay can be viewed as a straight line on a level versus time plot, and the slope of the line can be described either as a decay rate in decibels per second or as a reverberation time in seconds. The decay of the 250-Hz octave band of noise pictured in Figure has two exponential slopes.

The initial slope gives a reverberation time of 0.35 second and the final slope a reverberation time of 1.22 seconds. Exponential Decay This is a decay of an octave band of noise centered on 250 Hz in a 400-seat chapel, poorly isolated from an adjoining room.
Decays taken in the presence of acoustically coupled spaces are characteristically concave upward and often the deviations from the straight line are even greater.
When they depart from a straight line in a level versus time plot, we conclude that true diffuse conditions do not prevail. Spatial Uniformity of Reverberation Time The results of measurements in a small video studio of 22,000 ft3 volume.
Multiple reverberation decays were recorded at the same three microphone positions for both “panels-reflective” and “panels-absorptive” conditions.
The open and filled circles show the average values for the reflective and absorptive conditions, and the solid, dashed and dotted lines represent the average reverberation time at each of the three microphone positions. It seems reasonable to conclude that spatial variations in reverberation time are related, at least partially, to the degree of diffusion in the space. Spatial Uniformity of Reverberation Time For the “panels reflective” condition at 500 Hz, the mean reverberation time is 0.56 second with a standard deviation of 0.06 second.
For a normal distribution, 68% of the data points would fall between 0.50 and 0.62 second.
That 0.06 standard deviation is 11% of the 0.56 mean. Closer examination of the reverberation time variations of the data of Table.
The standard deviation, expressed as a percentage of the mean value, shows lack of diffusion, especially below 250 Hz.
For this studio for two different conditions of absorbance, diffusion is poor at 63 Hz, somewhat better at 125 Hz, and reasonably good at 250 Hz and above. Absorbent in Patches Consider the results of an experiment showing the effect of distributing the absorbent. The experimental room is approximately a 10-ft cube and the room was tiled.
For test 1, reverberation time for the bare room was measured and found to be 1.65 seconds at 2 kHz.
For test 2, a common commercial absorber was applied to 65% of one wall, and the reverberation time at the same frequency was found to be about 1.02 seconds.
For test 3, the same area of absorber was divided into four sections, one piece mounted on each of four of the room’s six surfaces. This brought the reverberation time down to about 0.55 second. Absorbent in Patches Significant result of distributing the absorbent is that it contributes to diffusion of sound. Patches of absorbent with reflective walls showing between the patches have the effect of altering wavefronts, which improves diffusion. Concave Surfaces Concave surfaces tend to focus sound.
Concave surfaces should be avoided if the goal is to achieve well-diffused sound. Convex surfaces tend to diffuse sound. Convex Surfaces : The Polycylindrical Diffuser Polycylindrical diffusers, when properly designed, are very effective at providing wideband diffusion.
(A) A polycylindrical diffuser reradiates sound energy not absorbed through an angle of about 120°.
(B) A similar fl at element reradiates sound in a much smaller angle of about 20°. Plane Surfaces Geometrical sound diffusing elements made up of two flat surfaces to give a triangular cross section, or of three or four flat surfaces to give a polygonal cross section, may also be used. In general, their diffusing qualities are inferior to the cylindrical section.
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