Modos Acustica Soluciones Faciles.pdf

PAPERS

A New Criterion for the Distribution of Normal Room Modes* OSCAR JUAN BONELLO

Solidyne S.R.L., Buenos Aires, Argentina

A new criterion is proposed for the best distribution of normal room modes, with the objective of improving the acoustics of recording and broadcasting studios. A new system is analyzed for controlling isolated room modes to obtain rooms i'ree of sound coloring. Applications are described, and the criterion is compared with others. A simple computer program performs the calculations.

0 INTRODUCTION The acoustical behavior of rectangular rooms has been the subject of several studies. These provide sufficient information to enable the acoustical design of small- and medium-sized rooms. Nevertheless, several parameters are not perfectly defined in terms ofevaluation criteria. One criterion, of utmost theoretical and practical importance, concerns the distribution of normal resonance modes in a given room. This matter is basic, particularly in the design of small broadcasting and television studios. The majority of sound studios are smaller than 120 m3, and the most common (and best studied) shape is the rectangular, with obvious building advantages. Other shapes have been tested, but their construction costs are higher and they have no advantage acoustically [I]. A rectangular room, subjected

to an acoustical

stim-

ulus, behaves like a large number of mutually coupled resonators. Tones whose frequencies do not correspond exactly to any of the natural modes (eigentones) of the room drive several resonators simultaneously. The initial modes are widely spaced in frequency, and their number increases with the frequency cubed. For acorrect reproduction of sound, we should have a large number of modes for each relative frequency interval (an octave, say). This requirement is fulfilled at medi-

* Presented at the 64th Convention of the Audio Engineerlng Society, New York, 1979November 2-5. J. Audio Eng. Soc., Vol. 29, No. 9, 1981 September

um and high frequencies or in large concert halls and theaters. But at low frequencies and in small rooms, the eigentone spacing is very large, usually greater than half an octave. This spacing leads to peaks and valleys in the response curve of the reproduced sound, since the sound is the sum of relatively distant modes which constructively or destructively interfere. This effect is characteristic of very small studios, particularly when they have long reverberation times. To eliminate or at least minimize the coloration, the eigentones should be spaced in order to avoid their concentration in some parts of the spectrum and their absence in others. The study of resonance modes and criteria for their spacing has been a classic subject in architectural acoustics [2]-[6]. Bolt [2]-[4], using the theory of numbers, recommended certain ratios between the dimensions, based on the concept of a frequency-spacing index. More recently a computer-aided analysis of the distribution of resonance modes led to differences with Bolt's recommendations while accepting part of his theory. These differences, marked by others [7], were recognized in practice by acoustical designers who used their own ratios derived from experience with good results [1], [7]-[9]. And yet, after 40 years of studies, and backed by theory, there were no valid empirical recommendations which could be used as guidelines for studio design. Our method is intended to fill this void by providing an easily applied criterion. The criterion is not statistical. It takes advantage of low-cost numerical computation provided by modern

0004-7554/81/090597-10500.75

© 1981 Audio Engineering Society, Inc.

597

BONELLO

PAPERS

calculators. It is based on calculus rather than prediction, and it uses analytical criteria that differ from their ancestors, 1 NORMAL

RESONANCE

MODES

Imagine a rectangular room extending in three dimensions, as illustrated in Fig. 1. In Cartesian coordinates the wave equation is O2P OX 2

+ --02P Oy 2

+ --02P + K2p = 0. OZ2

(1)

It can be shown [10], [11] that the pressure at any point in space, for the case of rigid walls, is [ n rrx I

{ n rry I

{_ n?z [

),

Accordingly, in a hall of 3000 m 3 we have 50 times as many modes as those present in a broadcasting studio of 60 m3for the same bandwidth and upper frequency. The influence of frequency is even more important than that of volume, since it appears as the square. It is for this reason that above 300 Hz sound coloring phenomena disappear. If a room is driven in a normal mode and the excitation source is then disconnected, the pressure decreases exponentially

e,_,,_,n =Ccos_W-x / cos__-_ ! COS

For low frequencies the density of modes can be calculated by means of the differences between values given by Eq. (4),or better,through a directprocessthat will be explained further on. Eq. (5) suggests the cause of coloring problems in small rooms at low frequencies. The density of modes increases with the room volume.

according

to the following equation

[5],

[III, Il2]: (2)

eJ2rrfnt

(6)

O.)nt

P" = K k e__:_,cos

J

where

where

f. = resonance frequency mode C = arbitrary constant

of the N(n,:n.:n:)

K

= constant representing androomvolume

k

= damping constant, tion

_(_,(,,, l_ = three dimensions of room ns, n.,,,n: = integer numbers 0, 1, 2, 3....

In addition, From Eq. (2) we can see that n, ny, n indicate the number of zero-pressure planes which are present along the three axes x, y, z. The values of the normal frequencies of the room are given by the expression

the steady-state

power, source location,

representing

sound pressure is given by

2Kto Pn max

=

(7)

44ton2

kn2 __ (to2

-t-

ton2)2

where to is the normal angular frequency 2 V/

I

+

+

(3)

_

where c is the velocity of sound (generally specified at 21°C as 344 m/s). Giving values to nx:n :nz starting from 0:0:0, the successive modes will be obtained. If Ix is the largest dimension, the mode of lowest frequency will be 1:0:0. The total number of modes between 0 and frequencyf will be, from [10],

Ns=

.__

v (5)3

+

___

s (f)2

+TT L

f

(4)

where

ONj _ 47rVf 2 Of C3

and to frequency is the driving angular The pressure versus curve can befrequency. seen in Fig. 2. If in Eq. (7) we find the points at which the pressure drops 3 dB (half-power), we have

Af

= f2 f_

k, n-

(8)

It is interesting to relate the coefficient k to the reverberation time RT. From Eq. (6) the time required for the pressure to drop 60 dB is T60 = 6.91/k, which, when substituted 6.91

in to Eq. (8), yields (9)

z

that is, the is

,/_

(5)

which shows that the density of modes increases with the frequency squared. Eq. (5) is valid only for frequencies high enough that statistical analysis can be applied. 598

of that mode

Asr-- rr T60

V = volume of room, = lxlylz S = internal surface, = 2(lxly + lxl_ + lylz) L = 4(l x + ly + 1,) The average density of eigenfrequencies, number of modes per hertz of bandwidth,

room absorp-

_'"-Y

ty Fig. 1. Rectangular room extended in three dimensions. J. Audio

Eng. Soc., Vol. 29, No. 9, 1981 September

PAPERS

A NEW CRITERION

showing that the bandwidth of the resonance modes is constant and independent of frequency if the reverberation time is also constant. The RT measured in a room is the average of the individual RT for each of the modes, but for practical purposes the RT used in Eq. (9) is the same when measured with pink noise. For rooms normally used as studios, the modal RTs are approximately constant with frequency. This constancy implies that the bandwidth will also be constant. For small rooms, the bandwidth given by Eq. (9) is between 3 and 10 Hz. In terms of relative bandwidth, measured in fractions of an octave and commonly used in electroacoustics, we have Af f

=

2 l/2n _

(10)

2 -l/2n

where 1/n is the bandwidth ,!

in octaves.

Taking into account Eqs. (9) and (10), we see that as RT increases, the bandwidth decreases. Rooms built with low RT in the bass, in accord with modern tendencies [13], will have wider bandwidths, advantageous for a larger number of responsive modes. On the other hand, for T,0 constant, the selectivity of the modes increases with frequency; the bandwidth in octaves decreases. This is not important at high frequencies since the number of modes increases rapidly, as we have seen; but conversely the bass end is enhanced, since the cctave bandwidth becomes large. For example, a typical value of At' = 5 Hz implies.a bandwidth of one-sixth octave at a frequency of 40 Hz, with the result that two or three modes within one-third sponse free of coloring.

octave will give a re-

2 CRITERION SELECTION An objective of the proposed criterion is to inform the designer whether or not the three dimensions for a 'given room are correct. If they are not, one or more of them should be changed, and the criterion applied once again. It should also inform the designer about the frequency band in which there will be coloring of sound in case the dimensions cannot be corrected. The first step consists of calculating, by means of a

P.max

OF NORMAL

ROOM

MODES

minicomputer or programmable calculator program, each of the lower resonance modes of the room. Eq. (3) is used for this calculation. It is not necessary to exceed a certain frequency or a certain order, due to considerations already noted and based on Eqs. (4) and (5). In the programs, which will be discussed later, the calculation is limited to the first 48 modes. Once the eigenfrequencies of the room are known, we analyze how many modes fall within each interval into which we divide the frequency spectrum. If we use the simplifying hypothesis that the ear is unable to discriminate modes within the interval, but only the sum of their contributions to the sound energy received within that band, it is necessary to know only the number of modes to obtain the total sound pressure. This implies that each mode, with its response to sound pressure given by Eq. (7) (Fig. 2), contributes in the same proportion to the band's energy, since it has the same maximum pressure and the same bandwidth given by Eq. (9). It is this concept of energy instead of frequency spacing that makes the criterion plausible. What bandwidth shall we choose'? Many arguments can be made in favor of narrow or wide bands. The value finally adopted is one-third octave. We use a relarive bandwidth, not an absolute one, taking into account the logarithmic characteristic of auditory perception and the ear's response to musical intervals. We are also influenced by electroacoustical experience which indicates the usefulness of one-third octave as a minimum unit of bandwidth. According to these concepts, tile number of eigentones falling within each one-third octave between 10 Hz and 200 Hz is calculated; this number gives the modal density function per one-third octave, D =F(f). The program plots modal density as ordinates and frequencies as logarithmic abscissas (the center frequencies of the one-third-octave bands). To analyze this curve, the following criterion is applied. 3 CRITERION For optimum room dimensions the following conditions should be met: 1) The curved = F(f) should increase monotonically. Each one-third octave should have more modes than the preceding one (or, at least, an equal number il' D = 1).

/'_

P.max i

\

/ f_

fn

f_

_f Fig. 2. Pressure versus frequency curve. J. Audio

FOR THE DISTRIBUTION

Eng. Soc., Vol. 29, No. 9, 1981 September

2) Thereshouldbenodoublemodes. Or, atmost, double modes will be tolerated only in one-third-octave bands with densities equal to or greater than 5. Subsequent experience led us to accept, although reluctantly, the condition that two successive bands can have the same number of modes with D greater than 1. This condition simplifies the requirements, even though conditions 1) and 2) of the criterion are to be preferred in the design stage. In Figs. 3 and 9 two computer

plots of curve D =

F(f) are shown. Fig. 3 shows a room that complies satisfactorily with the criterion, while the room of Fig. 9 does not, and its dimensions are not recommended 599

BONELLO

PAPERS

for this room volume. Because of the limited number of

if dimensions

calculated modes, the density curve increases up to a certain frequency and then begins to decrease. Accordingly, condition 1) should be applied only up to that frequency, The calculation program for this criterion is simple and can be run on desk calculators. Our program is run on an HP 9815 with printer 9871. Initially Eq. (3) is

corresponds exactly to the studio described by Knudsen, those dimensions become the best (Fig. 11). From these comparisons we observe a coincidence between the values recommendedby experience and those resulting from the proposed criterion. On the other hand, dimensional ratios once recommended, such as those of Sabine (2:3:5 and 1.6:3:4) [7], which

calculated, increasing coefficients nx:ny:nz one unit at a time. For example, after the value 3:0:0 we pass to 0:1:0 and then to 1:1:0. Thus n is increased in each subroutine, and once 3 is reached, the following digit advances, Coefficient n does the same with reference to n. The modes thus calculated are then printed. Finally all modes are classified in one-third-octave bands using the standard frequencies of ANSI S 1.6. Even if the caiculator lacks plotting facilities, the criterion can be applied using the number of modes in each band. It is also possible, in order to simplify calculations, to use

are no longer used, are really inadequate, as [.'ig. 12 shows. It is even more interesting to note that several optimum relationships exist, without fame and recommendation, obtainable when they are needed and for each particular room, through application of the proposed criterion.

Eq. (4) to obtain the number of modes directly as a difference between the frequency limits of each band, but this procedure is not as accurate as the use of Eq. (3). 4 COMPARING

DIFFERENT

CRITERIA

Over a period of four years, 35 broadcasting

studios

and recording rooms were successfully constructed uslng this criterion, and we believe that comparing it with other recommended and accepted parameters is important. First we analyze the ratio recommended by Knudsen [8] for small studios, 1:1.25:1.6. This same ratio was recommended by Olson [9] and others. In Fig. 3 the computer plot for a room of 60 m3 shows a perfect fulfillment of the criterion. In Fig. 4 various ratios are analyzed which are inside and outside of Bolt's chart. All ratios have been standardized for 60 m 3. Some comply with both criteria (such as(D and(D). Others are acceptable even though outside of Bolt's values(D or are not acceptable even though complying with Bolt's conditions O · The lack of correspondence for some values has been noted by other authors [7], [14] and is due, besides other factors, to the room volume, an important parameter which our criterion takes into account. Thus the same relationship can be acceptable for one size of room and unacceptable for another [''or example, consider the ratio 1:1.5:2.4 in Fig. 5, recommendedby Knudsen[8] for large studios. [.'ora volumeof 60 m3 this ratio is not acceptable.For a studio of 2000 m 3, for which it was recommended, it is satisfactory(Fig. 6), although not ideal. Conversely, the ratio in Fig. 3, acceptable for small studios, is also appropriate for 200 m3(Fig. 7)and for 400m3(Fig. 8). Another interesting example, which extends the series of satisfactory coincidences, is the ratio recommended by Knudsen for a large Hollywood studio, 1:1.45:3.27. Figs. 9 and 10 show that it is not acceptable for 60 m 3 nor for 2000 m 3. Nevertheless, and rather unexpectedly, 600

are increased to obtain the 4850 m 3 which

5 CONTROL

OF ISOLATED

MODES

There are cases in which the dimensions of a given room cannot be optimized for the simple reason that it is already built. It may not be possible even to modify its dimensions substantially. In these cases, undesirable modes can remain, and we are forced to minimize their RT. In other cases, as in new multitrack recording studies, it is convenientto havelow RT in the bass to optimize separation between microphones [13]. To achieve good control of low frequencies, resonator panels of special design are used [15] with an internal structure such as the one shown in Fig. 13. To achieve better control of certain modes, we locate these panels on the walls so that they coincide with areas of maximum pressure of the modal standing waves.A computerprogramwas written to plot Eq. (2). The resulting chart represents the intersections of surfaces of constant pressure with a plane parallel to the floor at a given height. At zero pressure the surfaces become planes and the intersections become straight lines. Fig. 14 shows the mode 2:1:0 for an experimental

Dimensions

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Meters

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69.08

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Eng. Soc., Vol. 29, No. 9, 1981 September

PAPERS

A NEWCRITERIONFORTHE DISTRIBUTION OFNORMALROOMMODES

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BONELLO

PAPERS

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X.

X'""_""_ x.....a-.''''_'''''_ 101 131 16L 20 _

251

321

401

501

631

......_'""_

801 100 J 125 I 1601

200 I

Fig 6 Calculation of resonance modes J Audio Eng Soc, Vol 29, No 9, 1981 September

PAPERS

studio.

A NEWCRITERIONFORTHE DISTRIBUTIONOF NORMALROOM MODES

In

this

n equals

mode

the same with

the plane

zero,

pattern is Not so with

and

the

at any height.

mode 3:2:2, which is shown at two different heights in Fig. 15. To show the effects of changing the locations of absorption panels within the experimental room (6.1 × 2.7 × 2.6 m), the RTs were measured for four panels in different positions, coinciding with maximum and minimum pressures (Fig. 14) for mode 2:1:0 at 85.08 Hz. The results are shown in Fig. 16 forasinusoidalstimulus. In Fig. 17 the results are shown using pink noise filtered by octaves. Above 500 Hz the panel locations do not produce significant changes, since at that frequency the field is sufficientlydiffuse. This technique of isolated-mode control, together with electronic or elec-

oi ....

ions

7.63

Modal

frequencies

x

3,3b

×

2.33

Meters

(Hz)

73._2 86.5_ 69._t 100.36 _0.73 133.57 169.57 175,46

147.64 22.54 154.37 67.63 1_.16 58.66 162.54 84.b3 _79.32 104.24 184.90 122.20 212.3_ 1_.32 217.11 166,97

sp..... I , , , _' _' _' Spectral density 18 1/3 12 il 10

7,._6 92.45 112.31 _2,.,_ 142.76 _71.07 182.56

_4,.35 4_.0, 162.39 50.89 15v.78 67.,9 170.18 101.78 la0.73 111.31 191.65 152.66 2i3.57 15_.1_ 222.88 0.00

100.11

I

_ I

_2' _

Ilil

il?

5.80

X

4.64

......

X-.,..';¢'"'

13 [

201

16j

freauencies 37.07

IHZ) 74.14

43.69

77.66

251

69.35 37.60 75.43 63.66 91.26

78.64 52.80 84.05 73.66 98.50

101.52 83.13 105.76 97.72 117.58

29.66 54.93 59.31 75.20 88.97

96.38 106.98

115.81 124.70

91.92 112.80

99.11 118.74

118.09 134.99

100.26 0.00

Modal

frequencies (Hz) 22,91 45.87 26.88 47.96 27.86 4_.52 31.20 39.08 41.52 52.72 54,55

Spectr_ 10'

]3'

×

x"

32m

40 m

501

63 L

80[ 10O I 125 [ 1601

10.87

X

200 I

modes.

of resonance

7.50

Meters

46.24

87.37 79.85 92.27 94.94 105.60

'

..

Dimensions 23.12

59.26 47.47 66.27 69.94 63.84

Spectral

......

9 Calculation

_Jg'

Meters

_'""x

24.52 Modal

X

.-_""...." l0t

X

i

,.

x'.,.-_

7.44

Iii

l_ " - '

:

obtain rooms dimensions. of the highest acoustical quality, even withreduced

Dimensions

Im 4111 JtJJllillJll

'

troacoustical techniques [16], enables the designer to

_,

Iii

_' _3 _ l_ _'

16'

m 'I

25 I

32 II

40111 50 I1,1111, 63 llillllJlfilllJlll 80 100

125 I

160 I 200 ,

50.51 55.72 57.46 66.01 67.40

7.01 21.04 17.31

23.98 31.13 28.73

46.40 50.46 49.02

14.03 15.62 21.15

26.33 32.41 38.00 47.99 51.93

34.92 39.71 44.39 53.18 56.76

52.89 56,16 59.57 66.36 69.28

31.65 34.62 47.47 49.50 0.0C

Spectr_

density I

, I

15 14 13

._ l' · '

12 11 10

%

;

10

I I, 16

[ 13

llll 20

Hi,I 25

Iltll, 32

lllllllllll_lt 40 I

Spectral density 15 14 13 :

:

_-

.. .... ·

201

251

9.37

321

Modal frequencies(Hz) 29.40 58.80 47.04 69.32 37.66 63.34 52.59 73.21 55.49 66.53 76.47 _4.82

75.32 83.79 91.87 98.94

X

401

501

831

801

of resonance

100 m 1251

1601

2001

X.....,K

modes.

10'

7.31

X

5.05

Meters

'°'

iDI

_''"'_'''"_

13'

16'

20'

18.36 55.07 29.84 59.89

34.66 62.43 41.89 66.71

61.00 80.56 65.94 83.93

36.71 23.53 43.61 47.06

50.51 72.44 72.94 89.53

58.45 78.18 70.64 94.23

77.52 93.30 93.69 107.1/

59.69 70.59 79.56 O.00

32.92 X

Modal frequencies(Hz) 17.10 34.19 20.04 35,76 20.75 36.16 23.23 37.64 29.07 30.89 39.20 40.56

32'

41.50 42.79 49.12 50.22

40'

50'

63 m

80 t

of resonance

14.63

X

10.06

......

lOO'

125

X''"'_

m 160'

200'

modes.

Meters

5.22 15.67 12.87 19.59

17.86 23.19 21.40 26,00

34.59 37.62 36.53 39.41

10.45 11.76 15.73 23.51

24.09 28.26 35.65 38.60

29.54 33.03 39.54 42.21

41.83 44.36 49,40 51.56

25.73 35.27 36.79 0.00

Spectr_

131

16 II

20 I

25 ,Il X21,11 40Ilji

Ii501illlllltllJ 0 I

il ilUt 1(_)l I

1_5 , _

I _

,

Spectraldensity

I

I

10 I ii

I

gl I

J

,.)_ ..' '

11 101 9 B 7 61

; .-

'

2 .'

il lO 9 8 _

"

161

201

251

401

160 i

200 I

60_

10OI 125 _

1601 2005

*' _.' .'

-.

321

100 I 125 I

...K'

....... .' ,-'

131

80 I

.-'

%

.X...-"'X'

3.

63 I

.

k

5, 4.

Iii50 'L

._

14. 13. 12q

l'

12.

IIil2gl Ut IIt IIII 121 IllmlllJltl41

Spectraldensity

14 13 12

lOI

251

10. Calculation

Dimensions

Spectrum

I

%

'_

..

Fig. Dimensions

:

._.. :' ." ". '

:

.F"

161

, 2U,.

% %

,.

7. Calculation

125 _ 160

il 10

.._"

131

, 1_ I

:'

k

_'l:'lg.

, 80

i2

"

101

Iii I 63

50

501

631

801

1001

125 I 1601

Fig. 8. Calculation of resonance modes. J. Audio Eng.Soc.,Vol. 29,No.9, 1981September

X,...._.-.

2001

101

131

-.

161

201

251

32_

401

501

631

Fig. l l. Calculation of resonance modes. 603

BONELLO

PAPERS

Dimensions

5.85

X

4.39

X

2.34

Meters

Dimensions

Modal frequencies (HZ)

6,30

X

3.79

X

2.5_

Meters

Modal frequencies (Hz)

73.50

147.01

29.40

149.92

5_.80

68,25

116.5!

2?.]0

1)0.21

54.60

94.13 83.29

158.33 152,14

68.21 48.98

114.82 80.33

171.44 154,95

39.18 70.66

87.41 81._

147.02 143.85

61;90 52.96

106.62 86.39

159.19 146.42

45.38 71.00

101.96 107.44

163.11 166.50

96.52 83.69

121.32 111.39

175.66 160.16

78.]6 97.97

96.49 113.56

153.67 163.93

93.64 94.76

115.67 116.60

_65.54 166.19

90.77 ' 105.92

122.48 116.63

176.66 188,22

117.96 121.16

139.01 141.71

188.50 190.50

117.54 131.43

126.01 152.30

172._ 192.80

122.26 1_._

140.02 154.73

183.25 194.72

116.15 166.69

150.59

197,10

146.95

164.31

207.66

0.00

161.79

200.3_

158._

172.93

209.47

0o00

79.17

Spectrum

I Spectral

73.5!

Spect rLum

lO I 131 density

WI

201

251

I

, I 44) , I 90 I

32

63

Il Ill_) lUll_lll ]JO0

II{ll{lll[,lll I_K TLql

_O0 ,

I Spectral

{,,il i.ii density

m'

_O ,

25 I

32

,

_

40

II 5C)

Il,Ill lOGIIIII I_KI_llll,llll 631{I Jan _

ur'in

15

15 14

_

13 12

.' ' .' %

11

·

lO

.'

14

'_

13 12

.." %.

11

y

'.

i

1o 9 8 ?

' X... .' ..''._'

101

131

161

201

251

.........

_

X

321

%

?......' .'

_

401

'

._"

.'

x'

;

.' ,'

·' .. x---.-_..... x'--'-_'-'--_'"'

;

%

.'

x..,.._....._....,_ ...._....._e ...,.x.. 501

631

801

1001

125 I

1601

2001

101

131

161

201

251

32'

(a)

401

501

631

BOJ

1001

1251

1601

MO I

:

(b)

Fig. 12. Calculation

of resonance

modes: (a) 1.6:3:4; (b) 2:3:5. WOODEN

RESONANT PANEL

,

OPENINGS

(ACUSTICAL

RESONATORS)

1.0f i

."'

i

%

..'''"°

''

.

O. 5{'

REINFORCING

Acoustical t standard

I

63

_

i

i

HZ

125

250

500

1000

Fig

2- 1-0

Fig.

CROSSPIECES

absorption curve of a '.. acoustical panel (S.A.P.) ......................

2000

4000

8000

'

604

,

14. Distribution

13

Internal construction

1_ _

ora standard

i

a

_

GLASSWOOL

acoustical pane]

F:ES.0BHZ

of several values of pressure (computer

output).

Room size 6.1 × 2.7 × 2.6 m; mode 2:1:0. J. Audio Eng. Soc., Vol. 29, No. 9, 1981 September

PAPERS

A NEW CRITERION FOR THE DISTRIBUTION OF NORMAL ROOM MODES

3- 2 - 2 F:2m_).Z2h_ 6,1x 2,7x 2.6meters(H= 1,20'm )

3 -2 - 2 F:_IB2._TJ(Z 6.1x 2,7x 2.6meters (H= 2,35 m)

p=0

p:0

j

J-h

w

Fig. 15. Two plots of the same room at two different levels, p = 0.6. AT

sec(,nds

%

15_

0

T

.......................

!

p=l

0,7.

J

p=0

_ Distance

Fig. 16. Variation of RT of mode 2:1:0 (85 Hz), measured with a sinusoidal source, due to the movement of 4 m 2 of panels (a = 0.3), which represents 20% of the total inside area of the room.

6 CONCLUSION We are confident that this criterion, easy to apply, will dispel part of the mystery in constructing recording rooms of medium dimensions. The criterion gives designers a new calculation tool which has proved its efficacy in four years of applications. 7 REFERENCES [1] C. L. S. Gilford, "Acoustic Design of Talks Studios and Listening Rooms," J. Audio Eng. Soc., vol. 27, pp. 17-31 (1979 Jan./Feb.). [2] R. H. Bolt, "Normal Modes of Vibration in Room Acoustics: Angular Distribution Theory," J. Acoust. Soc. Am., vol. 11, pp. 74-79(1939). [3] R. H. Bolt, "Note on Normal Frequency Statistics for Rectangular Rooms," d. Acoust. Soc. Am., vol. 18, pp. 130-133 (1946). [4] R. H. Bolt, "Normal Frequency Spacing Staffstics," J. Acoust. Soc. Am., vol. 19, pp. 71-90 (1947). [5] F. V. Hunt, L. L. Beranek, and D. Y, Maa, "Analysis of Sound Decay in Rectangular Rooms," J. Acoust. Soc. Am., vol. 11, pp. 80-94 (1939). [6] D. Y. Maa, "The Distribution of Eigentones in a Rectangular Chamber at Lower Frequency Ranges," J. Acoust. Soc. Am., vol. 10, pp. 235-238 (1939). [7] M. Rettinger, Acoustic Design and Noise Control, vol. I (Chemical Publishing Co., New York, J. Audio Eng. Soc., Vol. 29, No. 9, 1981 September

/-

4 m2 of soundabsorbers2 : : 1: 0

'inp

115

=

250

1

mode 2:1:0

540

l'k

2k

4k ' Hz

Fig. 17. Variation of the RT measured with pink noise, by octaves,for twodifferentpositionsof the absorptionpanels.

1977), p. 88. [8] V. Knudsen and C. Harris, Acoustical Designing in Architecture (Wiley, New York, 1950), pp, 402-403. [9] H. F. Olson, Music, Physics and Engineering (Dover, New York, 1967), pp. 302-303. [10] H. Kuttruff, Room Acoustics (Applied Science Publishers, Barking, Essex, England, 1976). [11] L. L. Beranek, Acoustics (McGraw-Hill, New York, 1954), ch. 10. [12] L. L. Beranek, Acoustics Measurements (Wiley, New York, 1949), pp. 329-336. [13] M. Rettinger, "On the Acoustics of Multi-track Recording Studios;" presented at the 49th Convention of the Audio Engineering Society, New York, 1974 September 9-12, preprint no. 795. [14] L. W. Sepmeyer, "Computed Frequency and Angular Distribution of the Normal Modes of Vibration in Rectangular Rooms," J. Acoust. Soc. Am., vol. 37, pp. 413-423 (1965). [15] O. J. Bonello, "A New Computer Aided Method for the Complete Acoustical Design of Broadcasting and Recording Studios;" Proc. Int. Conf. on Acoustics, Speech, and Signal Processing, ICASSP 79, Washington, 1979, pp. 326-329. [16] O. J. Bonello, "Modular Parametric EqualizerFilter; A New Way to Synthesize Frequency Response;" presented at the 55th Convention of the Audio Engineering Society, New York, 1976 October 29-Novembet 1, preprint no. 1170. 605

BONELLO

PAPERS

THE AUTHOR Il

Oscar Juan Bonello was born in Buenos Aires in 1940. He received an M.S. degree in electrical engineerlng from the National University of Buenos Aires in 1969. His early work at the University involved accidental printing in magnetic tapes, the Doppler effect and solid-state physics, In 1964 he founded Sistemas Solidyne, a company devoted to research in the electronics field and to the manufacturing of professional audio equipment. Mr. Bonello's work has included the design of audio,consoles and signal processors for recording, broadcasting and television studios, development of a method of studio acoustic treatment and collaboration in developing the Argentine telecommunications standards, Mr. Bonello designed the broadcasting network--

606

including all the audio systems--used during the satellite transmission of the 1978 World Football Games; 560 audio channels from five cities through three levels of control systems. The author of some 60 papers, he has several patents in his name. In 1973 he was awarded the Mencion de Honor in the National Prize of Industrial Design. He is a member of the Centro de Disefiadores Industriales and Professional Member of the CIDI (Center of Research in Industrial Design). A senior member of the IEEE, Mr. Bonello also is a member of the Audio Engineering Society, the American Acoustical Society, and the SMPTE. He is vice president and founding member of the Asociacion Argentina de Acdstica, and served as convention chairman of the last three Argentine Acoustical Conventions,

J. Audio Eng.Soc.,Vol.29, No.9, 1981September

In "A New Criterion for the Distribution of Normal Room Modes" by Oscar Juan Bonello (1981 September, vol. 29, no. 9) an error was printed in Eq. (7) on p. 598. The correct equation reads:

--

J. Audio Eng. Soc.. Vol. 29. No. 12. 1981 December