Building Utilities 3 Acoustics PDF

AR 335 BUILDING UTILITIES 3 ACOUSTICS AR. RODERICK G. TIAMSON, UAP, NAMPAP,INC.  AUDITORIUM ACOUSTIC An auditorium is a room, usually large, designed to be occupied by an audience which includes any room intended for: 1.Listening to music including theaters 2.Churches 3.Classrooms...

AR 335 BUILDING UTILITIES 3 ACOUSTICS AR. RODERICK G. TIAMSON, UAP, NAMPAP,INC.  AUDITORIUM ACOUSTIC An auditorium is a room, usually large, designed to be occupied by an audience which includes any room intended for: 1.Listening to music including theaters 2.Churches 3.Classrooms 4.Meeting halls Auditorium Acoustic - Background The design of various types of auditoriums has become a complex problem, because in addition to its various, sometimes conflicting, aesthetics, functional, technical, artistic and economical requirements Auditorium Acoustic - Background Hearing conditions in any auditorium are considerably affected by purely architectural considerations like: 1. Shape 2. Layout of boundary surfaces 3. Dimensions 4. Seating arrangements 5. Volume 6. Audience capacity Auditorium Acoustic - Background  Reflecting surfaces in a room are used to help the even distribution of sound and to increase the overall sound levels by reinforcement of the sound waves. The rules that need to be followed: 1. Reflections near the source of sound can be useful 2. Reflections at a distance from the source may be troublesome.  Plane reflectors are often suspended above a stage to give an early reflection into the audience and should be wide enough to reflect sound across the full width of the audience and the reflected sound must not be significantly delayed (figure 3).  Auditorium Acoustic - Background  At curved surfaces, the angle of reflection still equals the angle of incidence, but the geometry gives varying effects. Figure 4 illustrates the main type of reflection and Figure 5 shows the two types of curved surface. 1. Concave surfaces tend to focus sound-sound concentration 2. Convex surfaces tend to disperse sound.  Auditorium Acoustic - Background In auditorium, an echo is produced when the reflected sound wave reaches the ear just when the original sound from the same source has been already heard. Thus, there is repetition of sound and it is also called delayed reflection (Figure 6)  Auditorium Acoustic - Background The standing wave is a low frequency resonance that takes place between two opposite walls as the reflected wave interferes constructively with the incident wave. The resonant frequency depends on the distance between the two walls of the auditorium.  Auditorium Acoustic - Design 1. Shape  The shape of the hall plays a very important role in determining its acoustical quality.  The side walls and ceiling are potentially useful reflecting surfaces and should be carefully designed to maximize their usefulness.  The rear walls and floors are potential sources of useless and harmful reflections which are to be avoided.  Parallel hard walls create echo problems.  The fan shaped plan provides favorable reflection of sound from sides.  A concave surface within the hall is not desirable because it focuses sound reflections.  Such surface must be broken up with smaller convex surfaces so that sound is diffused in all directions.  Auditorium Acoustic - Design 2. Volume  The hall should be big enough so that sound intensity spreads uniformly over its entire area.  Smaller rooms lead to of sound because of formation of standing waves.  When the length of the hall, is very large in comparison to the longest wavelength of sound, the room is considered to be large in the acoustical sense and the sound within such a hall may be regarded as spread uniformly.  Auditorium Acoustic - Design  The floor area of the hall is computed, excluding the stage, based on the requirements of 0.6 to 0.9 m 2/person.  The height of the hall is determined by the presence or absence of the balcony, ventilation requirement etc.  An average height of 6 m for small halls and 7.5 m for large halls are usually adopted. It is desirable to provide slight increase in the height of ceiling near the center of the hall.  The recommended volumes for different types of auditoriums are as follows; (a) Concert halls 4.0 to 5.5 m 3/person (b) Theatres 4.0 to 5.0 m 3/persons (c) Public lecture halls 3.5 to 4.5 m 3/persons  Auditorium Acoustic - Design 3. Seating Arrangement The seats should be arranged in concentric arcs of the circles. Flat floor seating of more than a few rows is deprived of good visibility and good hearing. Sloped floor seating is essential for a large audience to have good visibility and good acoustics. The successive rows of seats must be raised over the preceding ones, with the result that the floor level rises towards the rear end. The rise in level may be about 8 to 12 m3 per row.  Auditorium Acoustic - Design The seats in each row should be staggered sideways in relation to those in front so that the line of sight of a person in any row is not obstructed by the person sitting in front. The back to back distance of chairs in successive rows should be at least 75 m3 and this may be increased up to 106 m3 for extra comfort. If balconies available it should not be too deep, sound shadow forms and the persons in the seats below the balcony do not receive ceiling reflections. Suitable sound reflectors should be positioned at appropriate places to get rid of this defect.  Auditorium Acoustic - Design 3. Seating Arrangement  Auditorium Acoustic - Design 4. Acoustic Treatment of Interior Surfaces The interior surface of the hall should be given utmost attention to make the hall acoustically satisfactory.  If the side walls are parallel, they are to be covered with absorbent materials. As the reflections from the near walls are of no use, the rear wall should be covered with absorbents. In many large halls, ceiling reflectors, sometimes called clouds is usually provided, are used to direct sound energy from the stage to seating area.  Auditorium Acoustic - Design The false ceiling positioned near the proscenium should be constructed of reflective material and inclined in a proper way to help reflections of sound from the stage to reach the rear seats in the hall. Concave shaped ceilings in the form of dome should be avoided. The rear portion of the ceiling may be treated with sound absorbing material so that build-up of audience noise is prevented.  The floor should be covered with a carpet. Carpet on the floor not only covers a useless reflecting surface but also greatly reduces audience noise. Auditorium Acoustic - Design 4. Acoustic Treatment of Interior Surfaces  Auditorium Acoustic - Absorption Auditorium Acoustic – Absorption Sound absorption and absorption coefficient change of sound energy into some other form, usually heat, in passing through a material or on striking a surface. The amount of heat produced by the conversion of sound energy into heat energy is extremely small. This phenomenon is called SOUND ABSORPTION. All the building materials absorb sound in some degree. Effective sound control of building will require the application of materials which are efficient sound absorbents, often termed “acoustical” materials.  Auditorium Acoustic - Absorption Auditorium Acoustic – Absorption In the various types of Auditoria, the following elements contribute to the overall sound absorption of the room: 1. The surface treatments of the room enclosures, such as walls, floor, ceiling 2.Room contents, such as the audience, seats, draperies, carpets, flowers, etc. 3.The air of the room.  Auditorium Acoustic – Absorptive Materials  The absorber performances are dependent on: 1. Porosity (i.e. the volume of pores connected to the outside air when compared to total volume of the material) 2. Flow resistance (movement of air particles within the material) 3. Structure factor (air channels running parallel to the surface have little effect 4. Mounting system: air space behind the absorbent material affects the frequency response of the absorbers.  Types of absorbers: 1. Porous absorber – The particles are interlocking and act by converting sound energy into heat - better absorption for high frequencies - E.g. fiberglass, mineral wool, glass wool, acoustic tiles, acoustic blanket, etc  Auditorium Acoustic – Absorptive Materials 2. Panel Absorber – Panel or membrane absorbers are constructed from fixed sheets of continuous materials with a space behind them; the space may be of air or may contain porous absorbent. -The panels absorb the energy of sound waves by converting them to mechanical vibrations in the panel which, in turn, lose their energy as friction in the clamping system of the panel. - Better absorption for low frequencies - -E.g. plywood and hardboard paneling, gypsum boards, suspended plaster ceilings, furred out plasters, rigid plaster boards, windows, glazing, doors, wood floors and plat- forms, etc.  Auditorium Acoustic – Absorptive Materials 3 Resonator – They consist of an enclosed body or air confined within rigid walls and connected by a narrow opening (called the neck) with the surrounding space in which the sound waves travel. -A cavity resonator of this type will absorb maximum sound energy in the region of its resonance frequency. -An empty jar bottle, also acts as a cavity resonator; however, its maximum absorption is confined to a very narrow frequency band (specific frequencies). Auditorium Acoustic – Absorptive Materials  TYPES OF AUDITORIUM TYPE OF AUDITORIUM 1. FOR SPEECH - Conference Hall - Lecture Theatre - Law Court 2. FOR MUSIC - Concert Hall - Music Practice Room 3. MULTI-PURPOSE - School Assembly Hall - Town Hall END Noise Reduction Coefficients Room Noise Reduction The buildup of sound levels in a room is due to the repeated reflections of sound from its enclosing surfaces. This buildup is affected by the size of the room and the amount of absorption within the room. Noise reduction can be found using the ff. formula NR = 10 log (a2/a1) Where: NR = room noise reduction (dB) a2 = total room absorption from treatment (sabins) a1 = total room absorption before treatment (sabins) Sample Problem A small room 10 ft by 10 ft by 10 ft has all walls and floor finished in exposed concrete. The ceiling is completely covered with sound-absorbing spray on materials. Sound absorption coefficient α’s is 0.02 for concrete and 0.70 for spray- on materials, both at 500Hz. a. Find the noise reduction NR in this room if sound-absorbing panels are added to two adjacent walls. The sound-absorption coefficient α is 0.85 for panels at 500Hz. b. Find the noise reduction if all four wall surfaces are treated with sound- absorbing panels and the floor is carpeted. The sound absorption coefficient of the carpet is 0.50 at 500 Hz. Solution: a. For Noise Reduction (NR) Compute the surface area s sc = 5 x 10 x10 = 500 ft2 (concrete area) sso = 10 x 10 = 100 ft2 ( spray-on material) Compute the total room absorption a1 with spray-on material on the ceiling. a1 = ∑sα = (500 x 0.02) + (100 x 0.70) = 80 sabins compute the total room absorption a2 with sound-absorbing panels covering two walls and spray-on materials on ceiling. a2 = ∑sα = (300x0.02) + (200x0.85) + (100x0.70) = 246 sabins compute the noise reduction NR NR =10 log (a2/a1) = 10 log (246/80) = 4.87 ~ 5 dB Without treatment at 4 walls, floors & ceilings ST = 6 x 10 x 10 = 600 ft2 a1 = 600 (.02) = 12 Without treatment at 4 walls & floors a2 = 500 (0.020) + 100(0.70) = 80 NR = 10 log (a2/a1) = 10 (log 80/12) = 8.2 ~ 8 dB b. For Noise Reduction (NR) Compute the total room absorption a3 with sound-absorbing panels on walls, spray-on materials on ceiling and carpet on floor.  a3 = ∑sα = (400x0.85) + ( 100x0.70) + (100x0.50) = 460 sabins Compute the noise reduction NR for these improvements compared to room conditions of spray-on ceiling treatment alone. NR = 10 log (a3/a1) = 10 log (460/80) = 7.59 ~ 8 dB Summary of Results Surfaces Treated (in addition to ceiling) Room NR (at 500Hz) Two walls 5 dB Four walls & floor 8 dB  SOUND ABSORPTION DATA FOR COMMON BUILDING MATERIALS Sound Absorption Coefficient NRC Materials 125Hz 250Hz 500Hz 1000Hz 2000Hz 4000Hz Numbers Walls (1-3, 9, 12) Sound-Reflecting 1. Brick, unglazed 0.02 0.02 0.03 0.04 0.06 0.07 0.05 2. Brick, unglazed and painted 0.01 0.01 0.02 0.02 0.02 0.03 0.00 3. Concrete, rough 0.01 0.02 0.04 0.06 0.08 0.10 0.05 4. Concrete Block, painted 0.10 0.05 0.06 0.07 0.09 0.08 0.05 5. Glass, heavy (large panes) 0.18 0.06 0.04 0.03 0.02 0.02 0.05 6. Glass, ordinary window 0.35 0.25 0.18 0.12 0.07 0.04 0.15 7. Gypsum board, ½ in thick ( 0.29 0.10 0.05 0.04 0.07 0.09 0.05 nailed to 2 x 4s, 16 in oc) 8. Gypsum board, 1 layer, 5/8 in 0.55 0.14 0.08 0.04 0.12 0.11 0.10 thick (screwed to 1 x 3s, 16 in oc with airspaces filled with fibrous insulation) 9. Construction no. 8 with two 0.28 0.12 0.10 0.07 0.13 0.09 0.10 layers of 5/8 in thick gypsum board 10. Marble or glazed tile 0.01 0.01 0.01 0.01 0.02 0.02 0.00 11. Plaster on brick 0.01 0.02 0.02 0.03 0.04 0.05 0.05 12. Plaster on concrete block (or 0.12 0.09 0.07 0.05 0.05 0.04 0.05 1 in thick on lath) 13. Plaster on lath 0.14 0.10 0.06 0.05 0.04 0.03 0.05 14. Plywood, 3/8 in paneling 0.28 0.22 0.17 0.09 0.10 0.11 0.15 15. Steel 0.05 0.10 0.10 0.10 0.07 0.02 0.10 16. Venetian blinds, metal 0.06 0.05 0.07 0.15 0.13 0.17 0.10 17. Wood, ¼- in paneling airspace 0.42 0.21 0.10 0.08 0.06 0.06 010 behind 18. Wood, 1- in paneling airspace 0.19 0.14 0.09 0.06 0.06 0.05 0.10 behind Sound-Absorbing : 19. Concrete block, coarse 0.36 0.44 0.31 0.29 0.39 0.25 0.35 20. Lightweight drapery, 10 0.03 0.04 0.11 0.17 0.24 0.35 0.15 oz/yd2, flat on wall (Note: Sound reflecting at most frequencies) 21. Mediumweight drapery, 14 0.07 0.31 0.49 0.75 0.70 0.60 0.55 oz/yd2, draped to half area ( i.e. 2 ft of drapery to 1 ft of wall) 22. heavyweight drapery, 18 0.14 0.35 0.55 0.75 0.70 0.65 0.60 oz/yd2, draped to half area 23. Fiberglass fabric curtain, 8 ½ 0.09 0.32 0.68 0.83 0.39 0.76 0.55 oz/yd2, draped to half area (Note: The deeper the airspace behind the drapery (up to 12in), the greater the low-frequency absorption.) 24. Shredded-wood fiberboard, 2 0.15 0.26 0.62 0.94 0.64 0.92 0.60 in thick on concrete (mtg. A) 25. Thick, fibrous material behind 0.06 0.75 0.82 0.80 0.60 0.38 0.75 open spacing 26. Carpet, heavy, on 5/8-in 0.37 0.41 0.63 0.85 0.96 0.92 0.70 perforated mineral fiberboard with airspace behind 27. Wood, 1/2-in paneling, 0.40 0.90 0.80 0.50 0.40 0.30 0.65 perforated 3/16-in-diameter holes, 11% open area, with 2 1/2 –in glass fiber in airspace behind Floors (9, 11) 28. Concrete or terazzo 0.01 0.01 0.02 0.02 0.02 0.02 0.01 29. Linoleum, rubber, or asphalt 0.02 0.03 0.03 0.03 0.03 0.02 0.05 title on concrete 30. Marble or glazed tile 0.01 0.01 0.01 0.01 0.02 0.02 0.00 31. Wood 0.15 0.11 0.10 0.07 0.06 0.07 0.05 32. Wood parquet on concrete 0.04 0.04 0.07 0.06 0.06 0.07 0.05 Sound-Absorbing: 33. Carpet, heavy, on concrete 0.02 0.06 0.14 0.37 0.60 0.65 0.30 34. Carpet, heavy, on foam 0.08 0.24 0.57 0.69 0.71 0.73 0.55 rubber 35. Carpet, heavy, with 0.08 0.27 0.39 0.34 0.48 0.63 0.35 impermeable latex backing on foam rubber 36. Indoor-outdoor carpet 0.01 0.05 0.10 0.20 0.45 0.65 0.20 Ceiling (6, 8-10) 37. Concrete 0.01 0.01 0.02 0.02 0.02 0.02 0.00 38. Gypsum board, ½ in thick 0.29 0.10 0.05 0.04 0.07 0.09 0.05 39. Gypsum board, ½ in thick, in 0.15 0.10 0.05 0.04 0.07 0.09 0.05 suspension system 40. Plaster on Lath 0.14 0.10 0.06 0.05 0.04 0.03 0.05 41. plywood, 3/8 in thick 0.28 0.22 0.17 0.09 0.10 0.11 0.15 Sound-Absorbing: 42. Acoustical board, ¾ in thick, 0.76 0.93 0.83 0.99 0.99 0.94 0.95 in suspension system (mgt. E) 43. Shredded-wood fiberboard, 2 0.59 0.51 0.53 0.73 0.88 0.74 0.65 in thick on lay-in grid (mtg. E) 44. Thin, porous sound-absorbing 0.10 0.60 0.80 0.82 0.78 0.60 0.75 material, ¾ in thick (mtg. B) 45. Thick, porous sound- 0.38 0.60 0.78 0.80 0.78 0.70 0.75 absorbing materials, 2 in thick (mtg. B) , or thin material with airspace behind (mtg. D) 46. Sprayed cellulose fibers, 1 in 0.08 0.29 0.75 0.98 0.93 0.76 0.75 thick on concrete (mtg. A) 47. Glass-fiber roof fabric, 12 0.65 0.71 0.82 0.86 0.76 0.62 0.80 oz/yd2 48. Glass-fiber roof fabric, 37 ½ 0.38 0.23 0.17 0.15 0.09 0.06 0.15 oz/yd2 (Note: Sound-reflecting at most frequencies.) 49. Polyurethane foam, 1 in thick, 0.07 0.11 0.20 0.32 0.60 0.85 0.30 open cell, reticulated 50. Parallel glass-fiberboard 0.07 0.20 0.40 0.52 0.60 0.67 0.45 panels, 1 in thick by 18 in deep, spaced 18 in apart, suspended 12 in below ceiling 51. Parallel glass-fiberboard 0.10 0.29 0.62 1.12 1.33 1.38 0.85 panels, 1 in thick by 18 in deep, spaced 6 ½ in apart, suspended 12 in below ceiling. Seats and Audience (1, 5, 7, 9) 52. Fabric well-upholstered seats, 0.19 0.37 0.56 0.67 0.61 0.59 with perforated seat pans, unoccupied 53. Leather-covered upholstered 0.44 0.54 0.60 0.62 0.58 0.50 seats, unoccupied 54. Audience, seat in upholstered 0.39 0.57 0.80 0.94 0.92 0.87 seat 55. Congregation, seated in 0.57 0.61 0.75 0.86 0.91 0.86 wooden pews 56. Chair, metal or wood seat, 0.15 0.19 0.22 0.39 0.38 0.30 unoccupied 57. Students, informally dressed, 0.30 0.41 0.49 0.84 0.87 0.84 seated in tablet-arm chairs 0.30 Openings (9) 58. Deep balcony, with 0.50 – 1.00 upholstered seats 59. Diffusers or grilles, 0.15 – 0.50 mechanical system 60. Stage 0.25 – 0.75  Miscellaneous (3, 9, 11) 61. Gravel, loose and moist, 4 in 0.25 0.60 0.65 0.70 0.75 0.80 0.70 thick 62. Grass, marion bluegrass, 2 in 0.11 0.25 0.60 0.69 0.92 0.99 0.60 high 63. Snow, freshly fallen, 4 in thick 0.45 0.75 0.90 0.95 0.95 0.95 0.90 64. Soil, rough 0.15 0.25 0.40 0.55 0.60 0.60 0.45 65. Trees, balsam firs, 20 ft2 0.03 0.06 0.11 0.17 0.27 0.31 0.15 ground area per tree, 8 ft high 0.03 66. water surface (swimming 0.01 0.01 0.01 0.02 0.02 0.03 0.00 pool) NRC (noise reduction coefficient) is a single-number rating of the sound absorption coefficients of the material. It is an average that only includes the coefficients in the 250 to 2000 Hz frequency range and therefore should be used with caution. See page 50 for a discussion of the NRC rating method. Refer to manufacturer’s catalogs for absorption data which should be from up-to-date test by independent acoustical laboratories according to current ASTM procedures. Coefficients are per square foot of seating floor area or per unit. Where the audience is randomly spaced (e.g. courtroom, cafeteria), mid-frequency absorption can be estimated at about 5 Sabins per person. To be precise, coefficient per person must be stated in relation to spacing pattern. The floor area occupied by the audience must be calculated to include an edge effect at aisles. For an aisle bounded on both sides by audience, include a strip 3 ft wide; for an aisle bounded on only one side by audience, include a strip 1 ½ ft wide. No edge effect is used when the seating abuts walls or balcony fronts (because the edge is shielded.) The coefficients are also valid for orchestra and choral areas at 5 to 8 ft2 per person. Orchestra areas include people, instruments, music racks, etc. No edge effects are used around musicians. Coefficients for openings depend on absorption and cubic volume of opposite side. Prepared by: Ar. Roderick G. Tiamson, UAP, NAMPAP, INC. College of Technology Department of Architecture University of San Agustin AR 335 BUILDING UTILITIES 3 ACOUSTICS AR. RODERICK G. TIAMSON, UAP, NAMPAP,INC. ROOM ACOUSTICS Room acoustic is a subject concerned with the behavior of a sound in an enclosed space and to provide best conditions for the production and reception of desirable sounds. ROOM ACOUSTICS ROOM ACOUSTICS ROOM ACOUSTICS  CRITERIA FOR SPEECH ROOMS The overriding criterion for speech is intelligibility. Since speech consists of short disconnected sounds 30 to 300 ms in length (see Section 26.17) among which are high- frequency, low-frequency phonemes, the ideal room music assure the ear’s undistorted reception of these phonemes. This require keeping reverberation to a minimum. We can obtain a good approximation of the subjective feeling of liveness of a room, for purposes of speech, from the relation 𝑉 TR = 0.3 log 10 where TR = optimum reverberation time in seconds for speech v = room volume, m3  CRITERIA FOR MUSIC PERFORMANCE Adequate design for a music space requires recognition of the following: 1. Large volume spaces require direct path sound reinforcement by reflection. 2. Relatively long reverberation time is needed to enhance the music – the exact amount depending on the type of music (see Fig. 26.25). Designers should keep in mind that recommendations vary as much as 100% between respected sources. 3. Directivity declines if the reinforcing signal is excessively delayed. With large resembles, directivity gives the sense of depth and in instrument location necessary for proper appreciation. This is often referred to as clarity or definition in music. With a solo instrument this problem is diminished. 4. Brilliance of tone is primarily a function of high-frequency content. Since these frequencies are most readily absorbed, a good direct path must exist between sound source and listener. Since our eyes and ears are close together, a good sound path exists when a good vision path exists. The actual design of music performance space is a very complex procedure involving extensive calculations of absorption, reverberation time and ray diagramming, and juggling materials, dimensions, and wall angles. Simulation techniques and acoustic model are also employed. Most modern design also uses movable reflectors panels and other active variables. After construction is completed, extensive tests are conducted and field adjustments are made. RAY DIAGRAM AND SOUND PATHS Ideally in every listener in a lecture hall, theater, or concert hall should hear the speaker or performers with the same degree of loudness clarity. Since this is obviously impossible by direct-path sound, the essential design task is to plan methods for reinforcing desirable reflections and minimizing and controlling undesirable ones. Normally only the first reflection is considered in ray diagramming, since it is strongest. Second and subsequent reflections are usually attenuated to the point that they need not be considered except for the special situation of flutter, echoes and standing waves discussed below. a.Specular Reflection. Specular Reflection occurs when sound reflects off a hard-polished surface. This characteristic can be used to good advantage to create an effective image source. In ancient Greek and Roman theaters, seats were arranged on a steep, conical surface around the performers. The virtue of the arrangement (see Fig. 26.28a) is that the sound power travels to each location with minimal attenuation. The same effect can be accomplished by placing the sound source above the seats. This is not practical physically, but it can be accomplished effectively by the use of a reflecting panel (see Fig. 26.28b b.Ray Diagrams. Ray diagramming is a design procedure for analyzing reflected sound distribution throughout a hall, using the first reflection only. Figure 26.30 shows a ray diagram. The rays are drawn normal (perpendicular) to the spherically propagating sound waves. Specular reflection is assumed. That is, the angles between the reflecting panel and the incident are reflected rays are always equal. Thus, in addition to the direct sound, each listener is receiving reflected sound energy. It is as though there were additional sound sources, the real one and numerous image sources. Figure 26.30 shows the application of a ray diagram to a lecture hall. In Fig. 26.30a the stage height and seating slope are arranged to provide good sight lines, and the ceiling height is established by reverberation requirements esthetics, cost and so on. It can be seen that less than half the ceiling is providing useful reflection. By dividing the ceiling into two panels (Fig. 26.30b) People in the rear of the room perceive the direct source plus two image sources, and the useful reflecting area is increased by 50%. In Fig.26.30c, the shape has been further refined to include a lighting slot and a loudspeaker grille.  Although they are a useful design tool, ray diagrams have certain restrictions. For example, the hall is three dimensional and the diagrams two dimensional, that is, sectional. To properly ray diagram, depth (width) must also be considered, and this unduly complicates the diagrams. Also, design must always be a compromise between ray diagrams for various “speaking positions” on stage. Thus, a paraboloid may be a perfect shape for one source position but will be c. Echoes As explained in Section 26.23, a clear echo is caused when reflected sound at sufficient intensity reaches a listener more than 50ms after he has heard the direct sound, Echoes, even if not distinctly discernible, are undesirable in rooms. They are annoying and make speech less intelligible. The relative annoyance is dependent on the time delay and loudness relative to the direct sound, which, in turn, are dependent on the size, position, shape, and absorption of the reflecting surface.  Typical echo-producing surfaces in an auditorium are the back wall and the ceiling above the proscenium. Figure 26.31 shows these problems and suggest remedies. Note that the energy that produced the echoes can be directed to places where it becomes useful reinforcement. If echo control by absorption alone were used on the ceiling and back wall, that energy would be wasted. The rear wall, since its area cannot be reduced too far, may have to be made more sound absorptive to reduce the loudness of the reflected sound. d. Flutter A flutter, perceived as a buzzing or clicking sound, is comprised of repeated echoes traversing back and forth between two non-absorbing parallel (flat or concave) surfaces. Flutter often occur between shallow domes and hard, flat floors. The remedy for a flutter is either to change the shape of the reflectors or their parallel relationship, or to add absorption. The solutions chosen will depend on reverberation requirements, cost, or esthetics. e. Diffusion This is the converse of focusing and occurs primarily when sound is reflected from convex surfaces. A degree of diffusion is also provided by flat horizontal and inclined reflectors (see Fig. 26.32). In a diffuse sound field, the sound level remains relatively constant throughout the space; an extremely desirable property for musical performances. f. Focusing Concave domes, vaults, or walls will focus reflected sound into certain areas of rooms. This has several disadvantages. For example, it will deprive some listeners of useful sound reflections and cause hot spots at other audience positions (see Fig. 26.33a). h.Creep This describes the reflection of sound along a curved surface from a source near the surface. Although the sound can be heard at points along the surface, it is inaudible away from the surface. Creep is illustrated in Fig. 26.33b. i. Standing Waves Standing waves and flutters are very similar in principle and cause but are heard quite differently. When an impulse (such as a hand clap) is the energy source, a flutter will occur between two highly reflective parallel walls. It is perceived as a slowly decaying buzz. When a steady, pure tone is the source, a standing wave will occur, but only when the parallel walls are spaced part at some integral multiple of a half-wavelength. When the parallel walls are exactly one-half wavelength apart, the tone will sound very loud near the walls and very quiet halfway between them. This is because at the center, the reflected waves traveling in one direction are exactly one-half wavelength away from those traveling in the other, and thus equal but opposite in pressure, which results in total cancellation. In other room standing waves are noted as points of quiet and maximum sound in the room. Standing waves are important only in small rooms with respect to the wavelengths generated (smallest room dimension