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# Room Acoustics (part 3)

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EXAMPLE PROBLEM (REVERBERATION TIMES)

The reverberation time in a 250,000-ft high school auditorium is calculated below for full and one-half occupancy conditions. An auditorium of this type, which serves many functions, must be designed with a compromise reverberation time. For example, a short reverberation time is desirable for speech activities and a long reverberation time is needed for instrumental music, chorus, and organ music. Consequently, a mid-frequency reverberation time of 1.8 s at 500 Hz is selected from the chart below. This reverberation time will be appropriate for music activities, where blending is needed, and will not be too long for speech activities, especially if a properly designed sound-reinforcing system is used.

Here are guidelines on how to select reverberation times at low and high frequencies. In this example school auditorium, the reverberation time at 125 Hz should be about 1 .3T = 1 .3 X 1 .8 = 2.3 s. If the preferred reverberation times from the table below can be achieved, the bass ratio there fore will be approximately 1.3. This ratio of low- to mid-frequency reverberation times is a very important characteristic of rooms where music is to be performed.

To find the required total absorption a, use the Sabine formula rearranged so:

a = 0.05/T

a = 0.05 x 250,000 / 1.8 = 6944 sabins at 500 Hz

 125 Hz 500 Hz 4000 Hz Preferred reverberation time (s) 2.3 1.8 1.4 Required total absorption from Sabine formula (sabins) 5435 6944 8929

Using the required absorption totals in the above table as a goal, calculate absorption a in sabins for all surfaces by multiplying given surface area in ft^2 times the respective sound absorption coefficient alpha. The table below shows the step-by-step computation process at sound frequencies of 125, 500, and 4000 Hz.

 125 Hz 500 Hz 4000 Hz Material Area (ft^2) alpha sabins alpha sabins alpha sabins Fully Occupied Ceiling: Gypsum board (in suspension system) 8150 0.15 1223 0.05 408 0.09 734 Side walls: Plaster on concrete block Rear wall: Thick fibrous blanket behind open facing Aisles: Carpet on foam rubber Wood Orchestra pit and apron: Wood Proscenium opening: (Moderately furnished stage) Air: (Coefficient per 1000 ft^2) Audience: Seated in upholstered seats (includes edge effect) Total absorption (sabins) One-Half Occupied Total absorption in auditorium less audience absorption from “fully occupied” computation Seats: Fabric, well-upholstered seats Audience: Includes edge effect Total absorption (sabins)

Finally, use the absorption totals (highlighted above) in the Sabine formula: T = 0.05V/a = (0.05 x 250,000)/a = 12,500/a to find the reverberation times summarized below.

 Reverberation Time (s) Conditions 125 Hz 500 Hz 4000 H Fully occupied 2.4 1.7 1.3 One-half occupied 2.5 1.9 1.4

Since the anticipated normal use condition will be between one-half and full occupancy, the above computations show that the auditorium satisfactorily meets reverberation time criteria.

OPTIMUM REVERBERATION TIME

The graph below presents optimum reverberation times at mid-frequencies (average of reverberation at 500 and 1000 Hz) for auditoriums with volumes of 10,000 to 1,000,000 ft. A deviation of as much as 10 percent from optimum reverberation generally will be satisfactory if other important attributes of room acoustics have been successfully achieved. For music perception, reverberation adds to the fullness of tone, blended sound, and richness of bass frequencies.

References

• L. L. Beranek, Acoustics, McGraw-Hill, New York, 1954, p. 425.
• L. L. Beranek, Music, Acoustics and Architecture, Wiley, New York, 1962, pp. 488-489.
• J. S. Bradley, “Uniform Derivation of Optimum Conditions for Speech in Rooms,”
• Building Research Note No. 239, National Research Council of Canada, November 1985.
• L. Cremer and H.A. Muller, Principles and Applications of Room Acoustics, vol. 1, Applied Science Publishers, Barking, England, 1978, pp. 610-627.
• V. O. Knudsen and C. M. Harris, Acoustical Designing in Architecture, Wiley, New York, 1950, pp. 375 and 394.

VARIABLE SOUND ABSORBERS

When the reverberation time must be varied to satisfy the requirements of different activities in a room, the sound-absorbing treatment can be designed to be adjustable. For most situations, listeners can detect a change in reverberation greater than or equal to 0.1 s. Surfaces or furnishings can be designed to expose either sound-absorbing materials (see column at left) or sound-reflecting materials (see column at right). In rooms for music, be careful to avoid placing absorption near the sources of sound where it can adversely affect early sound energy.

Retractable Sound-Absorbing Curtains

Curtains can be adjusted to vary the amount of absorption and , when stored in a recess, to expose a sound-reflecting backup surface. For music perception needs, curtains should be stored in a high transmission loss enclosure so they will contribute almost no absorption.

Note: A visually opaque, sound-transparent screen (called transondent) can be placed in front of curtains to allow changes in curtain extension without affecting appearance. This prevents the adjustment of the curtains for visual, not acoustical, reasons. Be careful where music perception is important because the deep airspace behind the sound-transparent screen could absorb too much low-frequency sound energy by acting as a volume resonator.

Sliding Facings

Two panels of perforated material can be used to vary absorption by sliding one panel in front of the other. The holes are lined up for maximum absorption and are staggered (or offset) for maximum reflection. The latter alignment blocks the path to the sound-absorbing treatment installed behind the panels.

Holes lined up to provide maximum absorption.

Hinged Panels

Sound-absorbing material installed on back of sound-reflecting panel can be swung into position to vary conditions from hard to soft.

Rotatable Elements

The details shown below are similar to the rotatable prism elements at l’Espace de Projection, IRCAM, Paris, France (V. M. A. Peutz, acoustical consultant) which have three sides: reflecting, absorbing, and diffusing.

Note: Variable absorption also can be used to adjust the reverberation during orchestra rehearsals in music halls so rehearsal conditions match performing conditions, when the audience is present.

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Updated: Friday, 2010-01-22 22:13 PST