Chapter 3 Room acoustics

Transcription

1 Chapter 3 Room acoustics Acoustic phenomena in a closed room are the main focal problems in architectural acoustics. In this chapter, fundamental theories are described and their practical applications are discussed.

2 What is the significance of Room acoustics?

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8 Significance of room acoustics The purpose of room acoustical design is to control the propagation, reflection and attenuation of sound within a space Direct sound Reverberant sound (reflections) Useful and harmful reflections Sound attenuation and absorption, diffusion Design goals according to the use of space, for example: Speech Good speech distinction (e.g. auditorium) / good speech privacy (e.g. open plan office) Music Appropriate reverberation and sense of space in the audience, stage acoustics which support music making

9 Significance of room acoustics Room acoustical design Design of sound reflections Design of sound absorption Design of the shape and geometry of the space Room acoustical design maximising the amount of sound absorbing material E.g. in a lecture hall the performer must be able to speak without restarining ones voice and so that the audience can distinguish what is being said Need for both sound absorbing and reflecting surfaces! Succesful room acoustics is, thus, a combination of the geometry of the space and the absorptive and reflective properties of materials

10 Examples of design goals Movie theater Hearing the sound track in the way the movie makers have intended it to be heard Concert hall Good spatial impression (sound surrounds the listener), sense of intimacy, warm sound color, adequate clarity, etc. Restaurant Peacefull acoustical environment (communication from short distance) Open plan office Speech sound distract concentration -> speech privacy between work places Factory Noise level may cause hearing damage -> design of effective sound absorption and noise blocking screens

11 Criteria for Good Acoustics Adequate loudness. -size and absorption (not too much of either) Uniformity -blending of stage sound, diffusion of hall sound (no dead spots) Clarity -needs sufficient absorption Liveness -feel that sound comes from all around Freedom from Echoes -too much separation in time of reflected sound

12 Seven objective room acoustics parameters REVERBERATION TIME (RT) EARLY DECAY TIME (EDT) STRENGTH (G) CLARITY (C) LATERAL ENERGY FRACTION (LEF) INTERAURAL CROSS CORRELATION (IACC) EARLY SUPPORT (ST early )

13 Reflection of sound Sound reflects at simplest as light: angle of incidence = angle of reflection (specular reflection), this applies when Sound wavelength is adequately smaller than the dimensions of the object causing the reflection The reflecting surface is even (not sound scattering) and hard (not sound absorbing) Sound reflection is complicated phenomenon and depends on frequency and the properties of the reflective surface

14 Significance of reflections Example: sound suddenly stops in a large concert hall Number of reflections occuring within the first 1 s is about 8000 As the number of reflections increases, there is a reverberant sound field in the space in which the listener cannot distinguish single reflections from one another; in large spaces this occurs after about 100 ms Sound field in a space comprises of three distinguishable parts: Direct sound Early reflections Reverberant sound field

15 Sound field in a room 1. Direct sound from source to listener 2. Early reflections within ms after direct sound 3. Gradually attenuating reverberant sound field

16 Sound field in a room

17 Reflection of Sound

18 Importance of reflections Sound perception is affected by the level of reflections, their delay in relation to direct sound and the direction from which they reach the listener. Strong reflections with adequate delay are heard as separate echoes (disturbance). If the delay between direct sound and early reflections is appropriate (about ms), the reflections increase the loudness of sound (perceived sound level) important in the design of speech and music spaces. Lateral reflections (reaching the listener`s ears from the sides) add to the sense spatial impression and broadening of the sound source crucial in the design of concert halls

19 The effect of basic room geometry

20 Example: Focusing Sound

21 Effect of Surface Geometry

22 Example: reflecting surfaces in a concert hall

23 A. Characteristics of the indoor sound field The characteristics of the indoor sound field are as follows. (1) The sound intensity at a receiving point remote from the source is not attenuated as much as in free space even if the distance is large. (2) Reverberation occurs due to the reflected sound arriving after the source has stopped. These two features are quite distinct from the outdoor situation and are very important. This is mainly due to the effect of the surrounding walls that determine the room shape. The purpose of the study of room acoustics is to control upon the room shape and surface finish, peculiar phenomena like echoes, flutter echoes, etc., which result in a complicated acoustic field by means of room boundary conditions such as room shape and finishing materials and to create a satisfactory acoustic environment in the space.

24 B. Geometrical acoustics and physical acoustics The science that handles sound energy transmission and diffusion geometrically without considering the physical wave nature of sound is called geometrical acoustics. Wave acoustics or physical acoustics is the science that handles the physical wave nature of a sound. When the wave nature of the sound field in a room is discussed, the wave equation, has to be solved under the appropriate boundary conditions. It is possible, however, to solve only simple cases. However, in the case of rooms with dimensions that are large compared with the wavelength and with a complexity of walls, the sound field may be analysed rather simply with geometrical acoustics and the wave nature of sound ignored. Thus, most practical problems of room acoustics are handled with the aid of geometrical acoustics although it is necessary to have a proper understanding of wave acoustics for more accurate and effective application of the former.

25 3.2 Normal mode of vibration in rooms When wave motion is taken into account in room acoustics, the most important and fundamental characteristic that needs to be understood is the normal mode of vibration of the room. Thus, to begin with, the simplest case of one dimensional space, i.e. the sound field in a closed pipe, is discussed. A. Normal mode of vibration in a closed pipe a. Wave equation and its solution In the case of a closed pipe whose internal diameter is small compared with the wavelength, the sound wave can only propagate longitudinally and not across the pipe, therefore, only one-dimensional plane wave motion need be considered. The wave equation of this free vibration is where ϕ can be thought of as either the sound pressure p or the particle velocity v because both can be expressed in the same form.

26 Instead of the double process of handling p and v, it is convenient to introduce a new function ϕ, which is defined as follows where ρ is the density of the medium. When the sound wave can be described by simple harmonic motion, the Equation (3.1) becomes or

27 b. Natural vibration in a closed pipe Here, we discuss the case where the pipe is closed at x = 0 and l x by rigid walls. The boundary condition of this space is such that the particle velocity is 0 at x = 0 and x = l x. From Equations (3.2) and (3.5) the following is obtained Applying the boundary conditions yields Where, m=0 is not our concern as it infers zero vibration. Then, the angular frequency with specific values is expressed as follows

28 And frequencies satisfying the above relation are These are called normal frequencies or natural frequencies characterising natural vibrations, which are also known as normal modes of vibration. Furthermore, at these frequencies the pipe resonates, therefore, they are called resonance frequencies. The wavelengths λ m for the above case are This means that the frequencies where the pipe length is an integral multiple of a half wavelength are natural frequencies. There are an infinite number of normal modes of vibration from m=1 to infinity.

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30 [Ex. 3.1] Obtain the normal mode of vibration m=1 to 3 for a pipe of length 6.8 m. Take sound velocity c=340ms 1 By using the formula of We get

31 B. Natural frequency of a rectangular room In ordinary rooms, the sound wave has to be treated as a three-dimensional field. The velocity potential ϕ is given as a solution of the three-dimensional wave equation similar to the one for the one-dimensional field as follows Where l x, l y and l z are dimensions of the rectangular room.

32 The boundary condition for a rigid wall is that the particle velocity normal to the wall is zero at the wall. The equation can be solved in a similar way to the one-dimensional case. With these conditions the natural frequency is obtained as follows. where n x, n y and n z are taken as 0, 1, 2, 3,..., etc. The particle velocity distribution in the room is expressed as a standing wave as follows

33 Although there are an infinite number of normal modes depending upon arbitrary combination of n x, n y and n z, they are separated into three categories: Good Room Mode Ratios 1: 1.3 : 1.6 1: 1.4 : 2 1: 1.6 : 2.2 1: 1.8 : 2.2 Axial mode (Two surfaces): for which two n s are zero, then the waves travel along one axis, parallel to two pairs of walls and are therefore called axial waves. Tangential mode (Four surfaces) : for which one n is zero, the waves are parallel to one pair of parallel walls and are obliquely incident on two other pairs of walls. The waves are called tangential waves. Oblique mode (Six surfaces) : for which no n is zero, then the waves are obliquely incident on all walls and called oblique waves.

34 Each axial mode involves only two opposite and parallel surfaces. Tangential modes involve four surfaces, and oblique modes involve all six surfaces.

35 As an example, let us assume that the z dimension, l z, is less than 0.1 of all wavelengths being considered. This corresponds to nz being zero at all times. Hence, Let l x =4 m and l y = 3 m. Find the normal frequencies of the n x = 1, n y = 1 and the n x =3, n y =2 normal modes of vibration. We have

36 The sound-pressure distribution in a rectangular box for each normal mode of vibration with a normal frequency w n is proportional to the product of three cosines: where the origin of coordinates is at the corner of the box. It is assumed in this eq. the walls have very low absorption. If the absorption is high, the sound pressure cannot be represented by a simple product of cosines. The angles θ x, θ y, and θ z at which the forward- and backward-traveling waves are incident upon and reflect from the walls are given by the relations

37 For the examples where n x = 1, n y =1 and n x = 3, n y = 2, the traveling waves reflect from the x = 0 and x = l x walls at Sound-pressure contour plots on a section through a rectangular room.

38 Sound-pressure contour plots on a section through a rectangular room.

39 Sound-pressure contour plots on a section through a rectangular room.

40 The wave fronts travel as shown in (a) and (b) of following figure. It is seen that there are two forward traveling waves (1 and 3) and two backwardtraveling waves (2 and 4). In the three-dimensional case, there will be four forward- and four backward-traveling waves. When the acoustical absorbing materials are placed on some or all surfaces in an enclosure, energy will be absorbed from the sound field at these surfaces and the sound-pressure distribution will be changed from that for the hard-wall case. For example, if an absorbing material were put on one of the l x l z walls, the sound pressure at that wall would be lower than at the other l x l z wall and the traveling wave would undergo a phase shift as it reflected from the absorbing surface.

41 Wave fronts and direction of travel for (a) n x =1, n y =1 normal mode of vibration; and (b) n x = 3 and n y = 2 normal mode of vibration. These represent two-dimensional cases where nz ¼ 0. The numbers one and three indicate forward-traveling waves, and the numbers two and four indicate backward-traveling waves.

42 [Ex. 3.4] When normal modes (2,0,0), (1,1,0), (2,1,0) exist, the sound pressure distribution can be described in a two-dimensional plane since nz = 0 in Equation (3.15). And the mode (2,0,0) is in one dimension corresponding to the case of m= 2 in Figure 3.1. These results are shown by contours of equal sound pressure in Figure 3.3. On the two sides of the zero contour line of sound pressure, i.e. the node of the standing wave, the sign is reversed as shown in Figure 3.1. For the sound pressure distribution, however, only the absolute values are given since the phase is of no interest.

43 Some interesting characteristics are illustrated by this example as follows: (1) the sound pressure is a maximum at the room corner for any mode; (2) when any one of n x, n y and n z is an odd integer, the sound pressure becomes 0 at the centre of the room and so on. C. Number of normal modes and their distribution The frequency of normal modes can be written as f n is found to correspond to the distance between the origin of the rectangular coordinates and the point given by coordinates

44 Thus, if a three-dimensional lattice spaced at c/2l x, c/2l y and c/2l z along the axes f x, f y and f z, respectively, as shown in Figure 3.4 is formed (called frequency space) then every node of the lattice in the frequency space corresponds to a normal mode, and the number of normal modes is equal to the number of lattice points. Figure 3.4 Frequency-space lattice showing the normal modes of vibration of a rectangular room.

45 The volume of the first octant of the sphere with radius f is (4πf 3 /3)/8= πf 3 /6 Each mode occupies a volume c 3 /(8 l x l y l z )=c 3 /(8 V) So, the number of oblique modes below f is approximately As far as the distribution of natural frequencies is concerned, the higher the frequency, the larger their density and since the number of oblique modes is largest, the density is considered to be proportional to the square of the frequency and at the frequency f the modal density is approximately

46 D. Room shape and natural frequency distribution Using, Depending on the particular choice of (n x, n y, n z ), it is possible to obtain the same value for the frequency f n with more than one combination of (n x, n y, n z ). These normal modes are then referred to as degenerate. Figure 3.5 Distribution of normal modes of vibration in two rectangular rooms. The degeneration of normal modes means that their non-uniform distribution makes the acoustic condition of the room undesirable and is related to the dimensional ratio l x : l y : l z.

47 In general, when the ratio of the room s length, width to height, is integrally related, e.g. 1:2:4, degeneration is emphasised and, therefore, must be avoided. The normal mode degeneration of a regular cube is very distinct. The room shape can be used to eliminate degeneration and to create a uniform distribution of normal modes by having oblique boundary planes instead of parallel walls. In such an irregularly shaped room all natural frequencies may be of the oblique mode type, favourable for a uniform sound decay process. This technique is often applied in reverberation rooms where the requirement is for a diffuse sound field.

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49 E. Transmission characteristics The natural frequency distribution can be obtained by measuring the transmission characteristics of the room. While generating a pure tone of constant intensity with a loudspeaker at one corner of a room and sweeping the frequency, the record of sound pressure level measured at another corner shows the transmission characteristics between the two points.

50 In general, a sharp peak can be found at the normal mode frequencies of the room. Although in the low-frequency range there are fewer normal modes yielding fewer resonance peaks they are, nevertheless, quite distinct. At higher frequencies there are many which are closer together, even overlapping and tending to produce a uniform transmission. It is desirable to avoid degenerate normal modes and to have a uniform distribution of modes with spacing as nearly equal as possible at all frequencies. The curve shows various profiles depending upon the positions of the sound source and receiver. All normal modes of vibration of the room can be observed when the sound source is located at a corner and the receiver is in the other corner along a diagonal of the room

51 F. Effect of absorption of walls In order to simplify the above discussion we assumed the surrounding walls to be rigid and their surfaces completely reflective. However, they also possess some sound absorption. Therefore, the normal modes of a room generally tend to shift towards lower frequencies, and the rugged profile of the transmission characteristics is flattened. If flat transmission characteristics are desired; it is necessary to select appropriate absorbing materials and construction effective for particular normal modes.

52 Reverberation time Assumption of diffuse sound field In geometrical acoustics the sound field in a room is assumed to be completely diffuse. This means: the acoustic energy is uniformly distributed throughout the entire room; and at any point the sound propagation is uniform in all directions. When the room dimensions become large, the normal modes in the low frequency range are sparsely distributed but their frequencies are below the range of audibility, while many normal modes build up in the audible frequency range.

53 What is Reverberation time? Standard reverberation time has been defined as the time for the sound to die away to a level 60 decibels below its original level. The reverberation time can be modeled to permit an approximate calculation. The reverberation time (RT) is the most fundamental concept in geometrical acoustics for evaluating the sound field in a room. The theory is based on the assumption of a diffuse sound field in a room, thus, regardless of location and effectiveness of absorbing materials and of the sound source and measuring points, the reverberation time has the same value.

54 Significance of Reverberation time The reverberation time in a space correlates rather well with the perceived clarity of speech or music: long reverberation the syllables in speech or separate musical notes attenuate slowly and mask each other

55 Significance of Reverberation time Too short a reverberation time is not desirable because in an overly damped space there are no useful reflections! In addition to appropriate reverberation time, good room acoustics provides that The space has appropriate size and shape Sound absorbing and reflecting surfaces are positioned correctly Two viewpoints: room acoustics experienced by the audience and by the performer For the audience, it is important to have useful sound reflections form the performer to the audience For the performer, it is important that the stage acoustics supports the performer`s activity

56 Example: To get good sound effect inside a hall a) The reverberation time has to be as large as possible. b) The reverberation time has to be zero. (c) The hall should not have any absorbing material. (d) The reverberation time has to be optimum.

57 Sabine s Formula for Reverberation Time Prof. Wallace C. Sabine (1919) determined the reverberation times of empty halls and furnished halls of different sizes and arrived at the following conclusions. The reverberation time depends on the reflecting properties of the walls, floor and ceiling of the hall. The reverberation time depends directly upon the physical volume V of the hall. The reverberation time depends on the absorption coefficient (A) of various surfaces such as carpets, cushions, curtains etc present in the hall. The reverberation time depends on the frequency of the sound wave because absorption coefficient of most of the materials increases with frequency.

58 Sabine summarized his results in the form of the following equation. Reverberation Time, T or Volumeof the Hall, V Absorption, A T = K V A where K is a proportionality constant. It is found to have a value of when the dimensions are measured in metric units. Thus, 0.161V T = A This Equation is known as Sabine s formula for reverberation time. 58

59 It may be rewritten as or T T S 1 1 N 0.161V 1 S 2 2 n S n 0.161V S n S n where S 1, S 2, are the areas of the various types of absorbing surfaces, and α 1, α 2, are the absorption coefficients of the respective surfaces. Sabine equation assumes that the sound field in the room is diffuse, i.e., at any point in the room sound can arrive from any direction and the field remains the same throughout the room This is an idealisation that does not hold perfectly true in real 59 rooms

60 Notes on Sabine equation Sabine equation can be used with good accuracy in rooms which are sufficiently reverberant Sabine equation is most accurate in a reverberant room where the average absorption coefficient is < 0,25) In very absorbent rooms the Sabine equation gives erroneous results Additional requirements for Sabine equation to yield accurate results: The room geometry should be simple (cube-like) and the room should be quite small The absorption material should be evenly distributed on the room surfaces Calculation error increases in large and complex spaces In rooms where all the absorption material is positioned only on one surface, Sabine equation yields shorter reverberation time than is the case in practice.

61 Example: Find reverberation time for a concert hall of dimensions 40 m*30 m *20 m having average absorption coefficent of 0.15.

62 Eyring-Norris equation Eyring-Norris equation: where V is room volume, S is the total surface area of the room and α average is the average absorption coefficient: For rooms with one or more very absorbing surfaces the Norris- Eyring equation usually gives a better RT value.

63 Example: Untreated Room: This example illustrates the implementation of Sabine s equation. The dimensions of an untreated room are m. The room has a concrete floor and the walls and ceiling are of frame construction with 1/2-in gypsum board (drywall) covering. As a simplification, the door and a window will be neglected as having minor effect. Size=23.3 x 16 x 10 m Floor : Concrete Walls/Ceiiling : Gypsum board, ½ in, on frame construction Volume: 23.3 x 16 x 10 m =3728 m 3

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66 Example: Calculate the reverberation time at 125 Hz, 500 Hz and 2000 Hz for a hall of 2500 m 3 to hold 250 people having the following surface finishes:

67 Notes on Eyring-Norris equation Eyring-Norris equation can be used in more absorptive rooms where average absorption coefficient is > 0.25, e.g., studios However, sound absorption coefficients that are commonly available and published by material manufacturers are Sabine coefficients (measured in a reverberation chamber and calculated using Sabine equation) and can, thus, be directly applied only to the Sabine equation For this reason, Sabine equation is the usual choice in acoustical design and is also used on this course Other researchers have suggested alternative reverberation formulas, e.g., Fitzroy, Millington, Hopkins-Striker...

68 Air absorption Taking account of air absorption, the Sabine and Eyring- Norris equations can be written as: where m is the air attenuation coefficient (some values: m = 0,009 at 2 khz; m = 0,025 at 4 khz; m = 0,080 at 8 khz) Air attenuation is only significant in large spaces above 2 khz depends on relative humidity of air, absorption increases at low humidity

69 Air absorption

70 Ideal Reverberation Times

71 CALCULATING REVERBERATION TIME

72 CALCULATING REVERBERATION TIME

73 Desirable reverberation times for various sizes and functions Variation of reverberation time with frequency in good halls

74 Acoustical characteristics beyond the reverberation time Liveness: A room is said to be live when the reverberation time is longer than the average for similar rooms. Intimacy: Refers to how close the performing group sounds to the listener. Intimacy is achieved whenever the first reflected sound reaches the listener less than about 20 ms after the direct sound.

75 Intimacy Refers to how close the performing group sounds to the listener. Intimacy is achieved whenever the first reflected sound reaches the listener less than about 20 ms after the direct sound. Subjective quality In concert halls, intimacy refers to the feeling of being close to the source of the music. This impression is usually present in smaller halls, but it is often difficult to achieve in larger spaces. In large halls that have not been designed with intimacy in mind, the audience may feel remote and detached from the performance.

76 Objective measure Intimacy is quantitatively measured by the initial time-delay gap (ITDG). This quantity is given by the time difference between arrival of the direct sound and arrival of the first significant reflection at a certain receiver position. If a space has a relatively short ITDG, it is said to be more intimate; a longer ITDG indicates less intimacy. In smaller halls, enclosing surfaces are closer together, so reflections occur more frequently than in large halls where surfaces are farther apart. Therefore, smaller halls generally have shorter initial time-delay gaps. Because the initial time delay gap can depend on receiver position, it is standard to measure ITDG at a position roughly in the center of a hall for comparison purposes.

77 Initial Time-Delay Gap One important characteristic of natural reverberation in concert halls was revealed by Beranek s study of halls around the world. At a given seat, the direct sound arrives first because it follows the shortest path. Shortly after the direct sound, the reverberant sound arrives. The time between the two is called the initial time-delay gap (ITDG), as shown in Fig..

78 Initial Time-Delay Gap If this gap is less than about 40 msec, the ear integrates the direct and the reverberant sound successfully. In addition to all of the reflections responsible for achieving reverberation density, the initial time-delay gap is another important delay that must be considered. In particular, this gap is important in concert-hall design (and in artificial reverberation algorithms) because it is the cue that gives the ear information on the size of the hall.

79 Optimum values Appropriate ITDG s depend on the type of music for which a space is being designed. However, in general, concert halls are more successful if they have shorter ITDG s, somewhere between 12 and 25 milliseconds. Solution To increase ITDG, one should shorten the distance from the first reflecting surface to the audience area. In larger spaces, this may be accomplished by adding ceiling reflectors or protrusions from the walls.

80 Fullness Fullness refers to the amount of reflected sound intensity relative to the intensity of the direct sound. The more reflected sound, the more full the hall will be. For slow, romantic music performed by vere large groups, fullness is required, whereas chamber music or music from the classical or baroque periods does not require great fullness. In general, greater fullness implies a longer reverberation time.

81 In general, greater clarity implies a shorter reverberation time. Subjective quality Clarity Clarity refers to how clear the sound quality is. Can you hear every separate note of a fast-tempo soloist s coda distinctly, or do the notes tend to blur into one another? Some blending is often desired for music, but for speech and opera, greater clarity leads to better speech intelligibility. Clarity, the acoustical opposite of fullness, is obtained when the intensity of the reflected sound is low relative to the intensity of the direct sound. Great clarity is required for optimum listening to speech and is particularly important when performing early orchestral music, such as the fast movements of the Mozart symphonies.

82 Objective measure: A popular objective measure for clarity is the Clarity index, C 80. This is defined as the logarithmic ratio of early sound energy, arriving in the first 80 ms, to late sound energy, arriving after 80 ms: C 80 = 10 log (early sound energy/late sound energy) The units of C 80 are decibels (db). C 80 is dependent upon frequency. Therefore, C 80 (3) has been developed to give an overall idea of what a room s clarity C 80 (3) has been defined as the average of C 80 values at frequency octave bands centered at 500 Hz, 1000 Hz, and 2000 Hz.

83 Optimum values In general, acceptable values for C 80 for concert halls are between +1 db and -4 db. How to design: To increase clarity, one should increase the amount of early sound energy relative to late sound energy. This could be accomplished by adding absorption in areas farther from the sound source.

84 Warmth Subjective quality Warmth is a term used to describe a cozy smoothness to the music. Warmth is obtained when the reverberation time for lowfrequency sounds is somewhat greater than the reverberation time for high frequencies. Its counterpart may be considered to be brilliance, which refers to a bright, clear, ringing sound. Either one of these qualities is desirable in moderation. If a sound field is too warm, the hall can be undesirably dark. With too much brilliance, the sound is harsh, brittle, and metallic sounding.

85 Objective measure Acousticians have determined that balancing warmth and brilliance is achieved by balancing the ratio of low frequency Reverberation Time (RT) to high frequency RT. Thus, the Bass Ratio (BR) has been suggested as an objective measure of warmth: BR = RT 125Hz + RT 250Hz RT 500Hz + RT 1000Hz where the numerator is an average of RT s measured in the 125 Hz and 250 Hz octave bands, and the denominator is an average of RT s measured in the 500 Hz and 1000 Hz octave bands.

86 However, the balance between warmth and brilliance should be kept in mind; excessive high frequency absorption will reduce brilliance unfavorably. Optimum values: A bass ratio between 1.1 and 1.25 is desirable in halls with a high RT, and a bass ratio between 1.1 and 1.45 is recommended for any hall with an RT of 1.8 sec or less. How to design: To increase the warmth, one should increase the low frequency RT while maintaining or decreasing mid to high frequency RT. One way to do this is to add materials in the space which absorb energy at high frequencies better than at low frequencies.

87 Brilliance Brilliance is the opposite of warmth and exists if the reverberation time for high frequencies is larger relative to that of the low frequencies. For an average room, the RT for the low frequencies is slightly greater than that for the high frequencies because of the absorption of higher frequencies by the walls, floor and ceiling.

88 Texture Texture refers to the temporal pattern of reflections reaching the listener. The first reflections should quickly follow the direct sound to achieve,intimacy, with successive reflections following quickly thereafter. To achieve good texture, it is necessary to have at least five reflections within 60 ms after arrival of the direct sound.

89 Texture Shown in figure below are two curves of sound intensity versus time. Figure (a) shows good texture whereas (b) shows poor texture owing to a late-arriving intense reflection.

90 Example: Which is not correct about the general requirements for the acoustic design of a room? a) Any intrusive noise should be avoided. b) Speech intelligibility should be satisfactory; c) Music should sound pleasing and have warmth. d) There should be no defects such as echoes or flutter. e) A uniform distribution of sound should be observed throughout the audiences. Solution: A uniform distribution of sound should be observed throughout the whole room.