Acoustic design for flexible membrane structures

Applied Acoustics 18 (1985) 399-433

Acoustic Design for Flexible Membrane Structures

Derek J. Croome

School of Architecture and Building Engineering, Claverton Down, Bath BA2 7AY (Great Britain)

(Received: 3 September, 1984)

S U M M A R Y

In the past twenty years various lightweight materials have become available which have strength and durability properties enabling structures having life spans of forty years to be built. Besides offering curved architecture, such structures are very sensitive to environmental change. Because of the differences in geometry, scale and materials which are inherent properties of lightweight membranes the soundJield has to be considered in detail. This paper reviews the current state of knowledge about the absorption and the sound transmission properties of flexible membranes and compares the results of work in America and West Germany with those obtained using a pneumatic airhouse at Bath University. The limitations of theory are discussed.

Theory shows that ~ = [1 +(~om/2pc)2] -~, and at 125Hz this compares with results for ct measured using a reverberation chamber technique; at higher frequencies there is not such a good agreement because the airflow resistance does not increase at the rate postulated by theory due to the nature of the .flexible materials. The usual practical sound reduction formulae, R = 14.51ogre + 10 Jor single layers and R = 20 log (m I + mz)d + 34 for double layers, are accurate enough for design calculations.

The variations in the reverberant field due to curvature were investigated. The centrifugal fan sound source was used to study the sound distribution throughout the airhouse. The traditional formulae for assessing fan sound power (i.e. L, .= 40 + 101ogQ + 201ogp) gave values which were 14 dB higher than those measured, but if these latter ones are used in the Jormula Lp = Lw+ 10log {(Q/4~r z) + (4/R)} with theoretical values of R then the agreement is reasonably close.

399 Applied Acoustics 0003-682X/85/$03-30 (~~ Elsevier Applied Science Publishers Ltd England, 1985. Printed in Great Britain

400 Derek J. Croome

Sound was attenuated at a rate o./'2 6 dB per doubling o f distance at lo w to high frequencies, respectively. Methods'.for avoiding sound focusing are discussed.

THE INTERACTION OF S O U N D WITH MATERIALS

Surfaces are defined acoustically as being hard and reflective or soft and absorbent; in between these extremes there are constructions with varying degrees of sound transmission. Sound energy incident upon a surface can be reflected (r) from it or absorbed (~) by it. The portion of the energy absorbed will be transmitted (z) to the other side of the surface and re- radiated into that space but some of the energy will be dissipated (6) as heat within the material from which the surface is constructed. The general power balance will be

l = r + 6 + r but c ~ = 6 + r Therefore

1 = r + c ~

Thin absorbent materials have high values of ~; the subdivision of this absorbent energy into 6 and z depends on the type of absorbent surface and material. Massive concrete or brick structures have a low value of c~ because they reflect sound back into the space, hence 6 and ~ are very small. For a structure with zero reflectivity and an absorption coefficient of unity the structure is said to match the sound field; the transmission of sound may be high, depending on the value of the dissipation coefficient.

For non-porous walls which are excited into vibration by the sound field (pressure, p) the velocity component (v) is identical to the velocity of the wall vibration. The wall impedance is defined as

Z = p_ /?

The specific acoustic impedance is the product of the air density (p) and the speed of sound (c). Thus, the specific acoustic impedance is defined as Z / p c and the reciprocal of this as the specific acoustic admittance.

An incident sound pressure wave can be expressed in the form

pi (x , t) =P0 exp [](cot - k x ) ]

and the particle velocity in this wave will be

vi(x, t) = Po exp [ j (w t - k x ) ] pC

Acoustic design for flexible membrane structures 401

The reflected wave will have a smaller amplitude and also undergoes a phase change ( + kx) . Hence, for reflection factor R

pr(x, t) = Rpo exp [j(cot + kx)]

and

vr(x, t) = - Rpo exp [j(cot + kx)]

The resultant waves in the plane of the wall (x = 0) will be the sum ofpi, vi and pr, vr:

p(0, t) =p0(1 + R) exp j ~ t

v(0, t) = P0 (1 - R) e x p j o t pc

but the wall impedance Z = p ( 0 , t)/v(O, t), giving

(1 + R) Z = pc (1 - R)

Therefore Z - pc

R - - - Z + p c

or, in terms of specific acoustic impedance, Z = Z/pc:

R _ Z - 1 Z + I

Acoustically hard structures have R = 1 or Z ,> pc whereas, for absorbent surfaces, R = 0 and Z = pc.

Now the sound absorpt ion coefficient is

e = l - R 2

( z - l) 2 c~ = 1 (Z -~- 1) 2 (1)

4 Re (X)

= IZ21 + 2Re(z ) + 1

Consider a thin partition wall of mass, m (kg/m2), vibrated by an acoustic wave having a pressure, P l, due to incidence and reflection in front of, and P2 behind, the wall. If the movement of the wall is v,

dv Pl --P2 = m - - dt

402 Derek J. Croome

For the characteristic impedance, pc and P2 = pcv. Therefore

dv p ~ = m ~7 + pcv or p l = (jcom + pc )v

where the wall impedance Z =j~om + pc (2)

Inserting eqn (2) into eqn (1) gives

[ (°°mlel-' (3) = 1 + \i)7pc I j

When the mass reactance of the wall is large compared to pc', the following approximation can be used:

ot = ( g P c ~ 2 (4)

Using eqn (4) for a plastered brick wall with m = 4 5 0 k g / m 2 gives = 8.8 x 10 -6 at 100 Hz. In the case of lightweight structures mwill be in

the range 0.5-2 kg/m 2, hence eqn (3) must be used. If m = 1 kg/m 2, pc' = 410 Rayls. Therefore

= [1 + 0.587 x 10 4j'2] 1 (5)

Notice that ~ decreases rapidly with frequency and this is the reason why the cracking of a whip sounds so sharp in a circus tent. At 100 Hz ~ = 0-63

TABLE 1 Theoretical Sound Absorption Coefficients for Unrestrained

Duraskin Membranes

Frequency (Hz)

lO0 500 l 000

Duraskin 18069 m = 0.245 kg/m 2 0,97

~ = [ 1 + 0 . 3 5 x 10 5j,21-1

Duraskin 18079 (perforated) m = 0.320 kg/m 2 0 9 6

c e = [ l + 0 . 4 2 x 10-s./ '2] 1

~ - [ 1 + 0 . 1 4 6 x 1 0 .*f2] J 0-873

Double layer

0.53 0 2 2

0"49 0-19

0.22 0.064


i .o- 3 PERFORATED DURASKIN FABRIC (18079)

o,. o~, Kg/m, / , S ' ~ . ~ , , , 7 iaJ

~ 50 mm air $gl~e x S I J % o . . , < , o ~ edge, i / !~ ,

~_ "+,,; 50...I _._,_o_,.,. ! \

1 5 )' O.,l-

i j ..A i o, / / " i / f /

/ / / / 2 layers, no I l r gap .- - ., _ . / ~ - - - - ~ . _ - : . ~ - ~ - 2 . - "

l iS 2SO SO0 IO00 :~00 40bO

FREQUENCY l o - b

DURASKIN FABRIC (18069) 0 . 245 Kg/m2

• I • t 50ram el, space t / / "~

-- closecl e d g e s ~ , ' 50ram/ 10 mmJ i o.- , oo.n edgN/ c,o..d~'"'7

/ e l l , no i i l gap

o ............ . 12S iSO SO0 tO00 2000 40DO

FREQUENCY

Fig. l(a) and (b). Values of absorption coefficient for Duraskin fabrics measured by Hoechst Aktiengesellschaft (Frankfurt, West Germany) in 1979 using impedance tube

method.

and at 1000 Hz e = 0-0168 for a membrane having a surface weight of 1 kg/m 2.

Using eqn (3), some theoretical values of the sound absorption coefficients for some Duraskin membranes are shown in Table 1. Test data obtained by Hoechst Aktiengesellschaft in 1979 using the impedance tube method is shown in Fig. 1 for various conditions. The effect of edge fixing and an air space behind the small sample are important parameters.

404 Derek J. Croome

In practice, the membrane will be extensive in area and the air either side will effectively extend to infinity. The maxima shown in Fig. I would be at lower frequencies, in agreement with theory, if the air space behind the sample were extended a much greater distance. The results indicate that, with an air space of 10mm, the frequencies at which the maxima occur increase. With no air space the sound is reflected off the sample.

Moulder and Merrill s have described some test results for three fibreglass fabrics (Structo. Fab 450, 375 and 120 produced by Owens Corning Fibreglass at Granville in Ohio) which have weights of 1.53 kg/m 2 (45 oz/yd2), 1.27kg/m 2 (37.5 oz/yd 2) and 0.407kg/m 2 (12oz/yd2). The two heavier fabrics are used as outer roof membranes and are completely coated to be impermeable so that the air flow resistance is effectively infinite and little sound absorption can take place. The lighter fabric is only lightly coated and is used as an inner liner; the air flow resistance was measured and found to be 2272 Mks Rayls and hence offers a high degree of sound absorption. It has already been established that the reflectivity is

For the light membrane,

R -

Therefore

Z - pc R - (6)

Z + pc'

2272 - 410 - 0-694

2272 + 410

c(=(1 -- R2) = 0 ' 5 1 8

The tests were conducted using a 6m 2 specimen mounted vertically between two reverberation chambers. Figure2 shows the sound absorption coefficients measured. Both heavier fabrics show a similar trend, with absorption coefficients ranging from 0.28-0-38 at 125 Hz to 0.06 at 4000 Hz. Table 2 gives a comparison between the theoretical (T) and the measured (M) values for various frequencies ( f ) .

The theoretical and measured values are comparable at 125 Hz for the heavier fabrics but at higher frequencies there is more absorption in practice than is accounted for in theory. For example, if the overall absorption coefficient is 0.1, then the reflectivity is 0.95 and the air flow impedance will be 16 000 Mks Rayls, which is very difficult to measure.

In the case of the porous liner material the effect of porosity is not taken


o.a- w o

0 ¢J o.s,

~ o.4- Q z

~ o.2,

Fig. 2.

, .. '~,~. poro¢lS mernb¢one 0.40T Kg//m ~

/ ""x /

:' /"- ..~..

/ - y

,,5 , - +** ,o** +g** ,,I,, ,~,, H!

FREQUENCY

Values of absorp t ion coefficient for Structo. Fab fabrics measured by Moulder and Merrill 8 using the reverberat ion chamber method at the Owens Corn ing Fiberglass

Technical Centre in G r a n t h a m , Ohio.

proper ly into accoun t in eqn (3). K u t t r u f f 7 p roposed a modif ied mass for inclusion in eqn (3):

m' - P° (b° + 2x) (7) (7

where b o = thickness o f mater ia l , x = 0"8r, r = radius o f each pe r fo ra t ion , ~ r = p o r o s i t y = S 2 / S ~, S 1 =cros s - s ec t i ona l area o f each hole and S z = m e m b r a n e area per hole.

T A B L E 2 Compar i son of Theoret ical (T) and Measured (M) Values of Sound Absorp t ion

Coefficient for Three Fibreglass Fabrics

Fabric Sound absorption coefficient

125 Hz 500 Hz 1 000 Hz

T M T M T M

Structo. Fab 120 [1 + 0.97 x 10- s f 2 ] - ~ 0.65 0.292 0.82 0.094 0-86 0.407 kg/m 2 = 0.87

Structo. Fab 375 [1 +0"947 × 10-4f2] -~ 0"38 0.041 0.17 0.0105 0.15 1'27 kg/m 2 = 0.39

Structo. Fab 450 [1 +0"138 x 1 0 - 3 f 2] 1 0.28 0.028 0.14 0.0072 0.08 1 "53 kg/m 2 = 0.32

406 Derek J. Croome

In the case of porous materials air is forced through the pores by pressure difference and has to overcome a flow resistance (r):

P~ - P 2 = rv

and since

P2 = Zt~

P l = ( Z + r)v

Cremer and Mfiller 2 show that

4 Z ( Z + r) a - - (2Z + r) 2

~ = ~ - - ~

4 Z r

( 2 Z + r) 2

(8)

(9)

(10)

Thus, when r = 2Z, 6 = 0.5; in addition, equal sound powers are reflected and transmitted.

In practice, wind forces can cause the lightweight membranes to move, thus reducing the relative motion in the pores which determines the friction losses and hence the value of the dissipation coefficient (6). It can be shown that the transmission coefficient is given by

( l / r ) 2 + (1/~om) 2

z = ( 1 / 2 Z + l / r ) 2 + ( l / t o m ) 2 (11)

and the absorption coefficient by

( 1 / Z r ) + (1/r 2) +(1/ogm) 2

= ( l / 2 Z + 1/r) 2 +(1 /o~m) 2 (12)

Sometimes lightweight membranes are insulated to limit heat loss and also, sometimes, condensation. Figure 3 shows the results for two conditions using (i) a double membrane with an impermeable outer fabric (1.5 kg/m 2) plus the inner porous lining (0.407 kg/m 2) with an air gap of 600 mm and (ii) a similar arrangement to (i) but with 50 mm of fibreglass insulation in the air space. Both solutions provide a high degree of sound absorption at low and high frequencies. The dip at 250 Hz occurs because


, ~ - O S "0" with SOmm of

U v.

.... /~m" l,$3Kg/m membrarm " ~

o,6-

i o.2-

o

,;, ,~ ',~ ,~'o ~ - -o ,'0° xz

FREQUENCY Fig. 3. Effect of double membranes and cavity insulation on sound absorption

(Moulder and MerrillS).

the air space distance (0.6 m) corresponds to the half wavelength (i.e. 0.66 m) at this frequency, i.e. a maximum sound pressure node.

The flow resistance of porous materials has been defined as

Ap r - (13)

u

or, for thickness, d, the specific flow resistance is

r' Ap (kg/m3s or Mks Rayls) (14)

Thus, when Ap is a maximum r' is large and air cannot enter the pores so that absorption is less effective.

The flow resistance also depends on the structure of the absorbent material as defined by the structure factor (~) and the porosity factor (o-). The flow resistance has, in effect, two components; one which is due to the increase of velocity as the air enters the pores and the other which is due to the structural geometry described by ~ and o- causing a frictional effect. At low frequencies the inertial effect becomes small whereas, at high frequencies, friction has a minor r61e to play.

The following ranges of flow resistance are recommended for absorbers:

High frequency absorbers 2pc < r < 4pc

Free hanging curtains pc < r < 2pc

Medium frequency absorbers r = pc

408 Derek J. Croome

Because of the pleated na tu re - -and hence irregular f o r m - - o f hanging curtains, no part is effectively located in a velocity nodal position, hence the optimum flow resistance is smaller.

Lightweight membranes have an important use as sound absorbers because their counterparts are perforated tiles which are more difficult to clean and are more susceptible to wear. It can be shown by experiment that the mass layers of perforated tiles or plates are equivalent to impermeable mass layers if the densities of these are low enough. This means that the currently available plastic membranes can be used and, by combining with different fibreglass layers, absorption throughout the high and medium frequency range can be achieved (see Fig. 4).

The resonant frequencies for the examples shown in Fig. 4 are in accordance with the equation

500 f - x/~d m Hz (15)

for d cm thickness of fibreglass layer; membrane weight m in kg/m 2 (0" 15) and porosity factor a = 0.9. For example,

500 f =

x/0-9 x 0"15 x 1"5

= 1111 Hz for 1 '5 cm mineral wool layer

Clearly, in such an arrangement one can design as much acoustical diversity as is required which will not be visually apparent.

In general, the resonant frequency of a system is proportional to the square root of the ratio of stiffness to mass. Because the stiffness of air layers is inversely proportional to its thickness, d, then, for normal incidence,

600 J = xfdm (16)

for dcm and m kg/m 2. Ifdm > 4 then one obtains a resonant system that absorbs preferentially at frequencies below 300 Hz.

In the case of double membrane constructions,

J = 850 + Hz (17)


0.8' U

O O.e-

~ O 4 -

~ o.2-

Fig. 4.

0,15 Kg/m 2 membrane

plus ;

x, ~ 7 0 m r n mineral wool

! x ' / / ~ ' ~ . ~ . . . . _ _ - ~ 30ram mineral wool

..- r , 7 " ~ \ ~-" / / ' . \ ~-- lS. .m m,.a,e, *ool

.." // "--.,\ i .: t / "-,X.\

... ,, / \ \ ,,,' / 1 '\, ,,, / /

,,' / / ~,, . . ,_ ..... / / "t ~'-:~:-.,_.

_ .,-"./,, \ "< -T, , < ' , , ~ , I l l lSO SO0 IOmOO ~t~OO 40~) 1300

HZ FREOUENCY

Absorption coefficients for fibreglass-covered membranes measured in a reverberation chamber (Cremer and MiillerZ).

For the case shown in Fig. 3 but with

d = 3cm

m 1 = 0-407 kg/m z

m 2 = 1.53 kg/m 2

Therefore

f = 850 Hz

This calculation has assumed that both membranes are plain whereas the lighter one is porous. The other condition that must be fulfilled is that

d < ~2 2800 < ~ f - ( d , 2 in cm)

Now, from Fig. 3 one can see that at resonance f = 850-1000 Hz, hence d < 2.8 to 3-3 cm. The tests conducted which produced the results in Fig. 3 used d = 60 cm. The reason for this restriction is that, if the air layer is to act as a spring coupler, then d must be effective but, at large distances, the membranes become acoustically separated.

410 Derek J. Croome

The resultant mass (m) should include the mass of the air in the perforations (ma), hence for a double membrane

1 1 1 1 - + +

m m a r?l 1 m 2

SOUND IN CURVED SPACES

One of the basic assumptions made in room acoustics is that the sound energy is distributed equally throughout the space. This is not true if some of the boundary surfaces are concave, as they are in the case of pneumatic structures. The ray diagram in Fig. 5 shows the effect of curvature on sound distribution along one elevational plane in the Bath Airhouse. The curves at the ends cause the reflected rays to be highly concentrated in these regions. As a result, this produces enhanced reverberation; values of this have been measured by Bellew. 1 In addition, as dimensions continually change the effect of wavelength becomes more important. Assuming the speed of sound is 330 m/s, then, at 125 Hz, the wavelength of sound is 2.64m and this reduces to 0"66 m at 500 Hz, 0-33 m at 1000 Hz and 0' 17 m at 2000 Hz. When the height of a structure tapers off at the perimeter and approaches the wavelength of a particular sound frequency then the surface generates diffuse reflections. When the wavelength is much greater than the dimensions of any obstacles in the sound path then they act as flat mirrors, whereas at very high frequencies when the wavelength is comparable with the size of surface details then each detail

® Effect of curved Surfaces o n S o u n d distribution

Fig. 5.

Whispering gallery effect

Effect of curved surfaces on the sound distribution in Bath University Airhouse.


. ~ . © @

~ ~© ,©

. ~ .G m© , ~ 'G n© , ~ ,@ 00 h~ h@ o©

Propagation of wsvefronta in a rectengulM room fo¢ s o u r c e ' S '

Propagation of • wavefront in a circular room between Source'S' end Receiver ~R'

Fig. 6. Sound distribution in rectangular and circular rooms (Cremer and Mfiller2).

acts like a small mirror. In this case the radius of curvature is usually much greater than the range of wavelengths encountered, which will be 0.1 to 0.5 m for speech and 0.3 to 3 m for ventilation system noise.

A comparison between sound propagation in a rectangular and a circular room is given in Fig. 6, as illustrated by Cremer and M/iller. 2 In the rectangular case the pictures depict eight instants, equally spaced in time, beginning with the direct sound moving from the source to the opposite corner (see a, b); at this stage the sound intensity varies throughout the space but with the successive arrival of wavefronts from source images of higher order and from greater distances (see c to h) the space becomes homogeneously distributed with sound energy. For the

412 Derek J. Croome

circular room the wavefront development is seen for successive arbitrarily chosen instants. Notice the strong concentration at R (see f) and then how a similar one occurs a little later at the source position S(see n). The sound distribution in this case remains inhomogeneous.

Sometimes sound in large spaces can be enhanced at distances a long way from the sound source. This is due to reflections skipping across the surfaces (see Fig. 5) and is commonly referred to as the 'whispering gallery' effect. The word 'whispering' is used because low level speech, for example, may not be heard properly near the speaker but may be heard clearly in a focusing region even if it is a long way off. Whispering is a form of speech behaviour used for privacy purposes but, because it contains mainly high frequencies, the sound is very directional and the wavelengths are always small compared with the size of reflecting surfaces. Clearly, the curved surfaces must be extensive and smooth; airhouses provide just the opportunity for the whispering gallery effect to occur. Some measurements confirming this in the Bath Airhouse have been made by Bellew. 1

In order to determine whether a curved surface will cause problems, it is necessary to ascertain if any reflections from the curved section are weaker than ones from an equivalent flat ceiling. This occurs if the centre of the dome lies higher above the floor than halfway to the ceiling, a condition which can be proved using optical ray acoustics and can be expressed as

h

2

for a dome of radius r, the centre of which is h above the source plane near ground level. During the Renaissance domes respected this rule because of the structural limitations. Today, the elegance of form and the simplicity of construction of shallow domes having a radius of curvature between hi2 and 2h means that there can be serious problems as regards focusing.

Methods of avoiding focusing include the use of absorbent material, faceting the surface and by making the visual domed surface acoustically transparent (see Fig. 7). Increased absorption reduces the reverberation time and this is often a disadvantage in places where music is performed.

Breaking up the curved surface into sound scattering elements provides an opportunity for aesthetic ingenuity. One needs to remember that the wavelength of sound extends from about 0.1 m at high to 3 m at low frequencies so the design needs to embrace this wide range of dimensions.


\/

® @ (9 Fig. 7. Methods for avoiding focusing by (a) absorption, (b) breaking up the curved surface and (c) making the domed surface acoustically transparent (Cremer and Mfiller 2).

The Aula Magna auditorium in Caracas has a concave ceiling and the architects engaged the sculptor-artist Alexander Calder to design the shapes and the colours of the convex reflectors in conjunction with the acousticians. Hans Scharoun used a tent shape for the Berlin Philharmonic Hall but he originally considered using a dome.

Separating the visual at acoustical boundaries is an idea which has been used in the design of planetaria. Clearly, there are possibilities here for using thin membranes which have high sound transmission coefficients and have sound absorbent areas behind them. The use of this method will depend on whether it is more important to have natural light from the ceiling or to have good acoustics such as those required for music. Another possibility is to let natural light enter through glass walls but have the reflective-absorbent opaque roof to satisfy the sound requirements.

Spaces are designed to avoid echoes. Listeners perceive sounds which arrive after the direct sound as echoes if this time delay is more than about 100 ms. The reflections must also be strong enough to combat with other simultaneous sound impulses. People speak at an average rate of five syllables per second (i.e. one every 200 ms); successive musical sounds can proceed at a much faster or slower rate than this. Sounds are localised according to the signal which reaches the listener first, even ifa succeeding signal is 10dB stronger and arrives within 50ms. In practice, it is necessary to allow for subjective variation, hence the time delay of 50 ms is also accepted as the limit before echoes are sensed. This corresponds to a path difference of 17 m between the direct and the indirect sound paths;

414 Derek J. Croome

Fig. 8.

/ ' I / , I / " , - ~ - 2h

Flutter echo in Bath University Airhouse (Bellewl).

useful sound reflections will occur from surfaces within 8.5 m, plus half the direct pathway, of the source. Curved surfaces produce zones of high reverberant energy and thus erroneous location can occur. A famous example of a long delayed echo reinforced by focusing is the Royal Albert Hall, in which the path difference between the ceiling reflected sound and the direct sounds is 60m, corresponding to a time delay of 167ms. Sometimes there is a succession of impulses or echoes termed multiple reflections, a famous one being the 'picket fence' echo which occurs in the amphitheatre at Epidaurus when empty, due to the sequence of reflections which arise from the regularly spaced banks of seats.

Repetitive reflections can happen when the same ray path is traversed several times and in smaller spaces this can sound like the fluttering of a bird, hence the term 'flutter echoes'. In the Bath Airhouse, Bellew 1 observed a flutter echo which occurred across the narrow section which corresponded to a vaulted ceiling above an earth floor (see Fig. 8). An explanation of this phenomenon is now given.

The radius of curvature of the ceiling in the airhouse is approximately equal to twice its height (r = 2h) so the ceiling acts like a parabola. A sound under the centre of the vault is reflected from the ceiling as a set of parallel rays which, after reflection at the floor, return to the ceiling; this focuses the parallel rays back to the original source point. The process repeats itself so that the echoes heard are first weak (parallel rays) then strong (focused rays). If the listener moves off centre the weak reflections may even become inaudible. The case is shown in Fig. 9(a) for an eccentric source, A, emitting sound to the ceiling at B, where it is reflected as parallel rays to the ground at C; these rays are reflected back to the ceiling, which focuses them back on to the floor at E symmetrically opposite the source. The process then reverses so that after eight traverses between floor and ceiling the rays return to the initial source position. It can be

Acoustic design f o r f lex ible membrane structures 415

Q ® D

I B ' II '

I I I I I I I I I I I / / I . " i I I 1 1 t

i i

Fig. 9.

© I i

Ray paths between vaulted ceiling and plane floor (Cremer and Mtiller2). (a) r = 2h, (b) r = h, (c) r = 4/3h.

shown that when r = h, a real flutter echo only occurs when the source and the receiver are at the centre (see Fig. 9(b)). When r = ~h the ceiling acts approximately elliptically and flutter echoes will occur (see Fig. 9(c)). In the case of the airhouse the floor is not highly reflective, especially at higher frequencies, so that the echoes will have a modified spectrum compared with the source.

The shape of a surface on which sound is incident is also important from another point of view. Convolute forms disperse the sound and assist in producing a diffuse sound field but they also present a varying incidence angle (0) for the sound. Walt impedance is not only a function of frequency but also depends on the angle of incidence, so that the impedance is modified to Z/cos 0. An example of this is shown in Fig. 10, which shows that as the angle of incidence increases and approaches grazing incidence the absorption coefficient increases, especially above 45 °, and the trend is more marked for lower frequencies. Flexible structures offer contour variations which cannot be achieved in traditional buildings but, in addition, variable absorption can be used in conjunction with solar protection blinds, thermal insulation or air

416 Derek J. Croome

Fig. I0.

3000Hzi'--'-" ~ I _ / ' ~ 1 / I

0 ° 10 ° 20 ° 30 o 4.0" 50 ° 60 ° 70 ° 80 ~

AhGLE OF INCIDENCE, 0

Dependence of absorption coefficient on the angle of incidence (Cremer and Miiller2).

recirculation tubes used to redistribute stratified air. There is a good opportuni ty here for aesthetics and function to be harmoniously combined.

S O U N D I N S U L A T I O N C H A R A C T E R I S T I C S OF L I G H T W E I G H T M E M B R A N E S

The sound absorption coefficient has already been defined as

When ~ is low then the sound dissipation in, and transmission through, the material is small but high values of ~ usually result in appreciable values of r depending on 5. The sound reduction index (R) of a structure is defined by the difference in sound level across it thus:

R = 10log - 10log

for the incident and transmitted sound pressures, Pi and Pt, respectively:

10,o t )


or, in terms of z,

R = 10 log ( ! ) (18)

When 6 is small ~t = z and so z can be assessed using eqn (3). Most absorptive wall coverings are backed up by a rigid wall so z ,~ 6 or

z ,~ r (reflection); ~ and 6 are very similar for such situations. Heavy curtains and membrane fabrics show significant differences between ~, 6 and T, and these can be calculated using eqns (8), (9) and (10).

Using eqn (3)--and hence the results for ~ = z in Table 2- -a comparison can be made between theory and the measurements made by

TABLE 3 A Compar ison of Theoretical and Measured Values of Sound

Reduction Index

Material Sound reduction index (R (dB)) weight (kg/m) 100 Hz 1000 Hz

Theory ~ Measured Theor) ,a Measured

0.407 0.41 4 10.26 6 1.27 2.92 5 19.9 16 1.53 3.77 7 21.4 17

"R = 10 log(l /z) and r = ct; ~ values are given in Table 2.

Moulder and Merrill 8 as shown in Table 3. The theory becomes limited for very light materials at low frequencies but, in general, there is reasonable agreement and hence eqn (3) gives a good approximation for estimating the sound absorption coefficient of lightweight fabrics.

Measurements of the sound reduction index were made by Moulder and Merrill 8 for three fibreglass materials discussed earlier and the results are shown in Fig. 1 l(a). The two heavier fabrics (1.27 and 1.53 kg/m z) provide similar sound insulation values of about l0 dB at low frequencies (250Hz) to 20dB at higher ones (2000Hz). The light material (0.407 kg/m 2) can only offer 5-10 d B of insulation and is little better than an open window. The effect of increasing the dissipation of sound energy by using a double membrane and putting 50 or 100ram of fibreglass material in the cavity is shown in Fig. l l(b). A double membrane construction improves the single fabric performance by 5dB, i.e. the

418 Derek J. Croome

x

~,o

~ 0 ,

Fig. l l(a).

.x

. x - " " [ ~ f

, . * ~ ¢ f

F41btic weight 1.53 Kg /m z ~ - - ' : ~

. . ' ' " ~ f " 1.27 K g / m '

. . - ~ . - - - - - ° I o.4o? ~ I . ,

i+~ ~+---=-- +--*--+ o---- 1 1 +

' ' ' O0 . . . . . 0 ' " 100 125 2';0 500 1 0 20 0 4000 6300

Frequency (Hz)

Sound reduction index for Structo. Fab materials (Moulder and MerrillS).

6 0 -

50-

40.

30-

2 O - x

10-

w 0 0

Fig. ll(b).

j o

o/" / (b)

I.o I ,~

©I, ~ °I" ~

aS [b) but 100 mm / / + / / Cavity insulation j o ~ A ~

(b) as (el plus 50ram I ~ " ' " Cavity insulation 7. Or ~ _ . = I "

7 / ~ . x - - "

0 - - - - ~ . . - - ~ ('a') double membrane J ~ ) '-" " ~ - " - 2 ;1~j ..~.. - .- ..... ,53 ~glm, + o 40, ~glm

o..a~- o - ~ f

, , . i i ' ~O 100 125 250 500 1000 2000 4000 63 0

Frequency (Hz)

Sound reduction index for Structo. Fab materials (Moulder and MerrillS).

heaviest fabric plus the light porous liner provide 14dB at 250 Hz and 25 dB at 2000 Hz. Insertion of 50 mm of insulation in the cavity increases these values to 15dB (250Hz) and 34dB (2000Hz) and 100mm of insulation gives 17dB (250Hz) and 41dB (2000Hz). Clearly, the insulation has thermal advantages but until a range of transparent insulation is developed the natural lighting will be reduced.


TABLE 4 Comparison of Sound Reduction Index Calculated Using Equations (19) and (20) and Measured for Single and

Double Membranes

Fabric weight Sound reduction index (kg/m 2) (R (dB))

Measurement at Theory 400 Hz

0.407 5 4.34 1.27 10 11.51 1.53 11 12.68

0.407 + 1'53 17 13.7 plus 50 mm air space

0'407 + 1.53 21 19.8 plus lOOmm air space

It can be shown that, in practice, for a single layer (see Croome 3)

R = 14.51ogm + 10 (19)

and for a double layer

R = 20 log(m 1 + m2)d + 34 (20)

for masses of each layer, rnl and mE, separated by distance d (in metres). Applying these formulae to the results of Moulder and Merrill, 8 a comparison can be made between traditional design theory and measurement, as shown in Table 4.

It can be seen that eqns (19) and (20) can be used to assess sound insulation with sufficient reliability.

THE BEHAVIOUR OF S O U N D SOURCES W I T H I N L I G H T W E I G H T STRUCTURES

The degree to which fan-generated noise needs to be controlled in an airhouse will depend upon the airhouse occupancy, the level of speech communicat ion required and the structure location. Where the structure is to be used as a warehouse, for example, high levels of noise and long reverberation times can be tolerated. For other applications such as

420 Derek J. Croome

offices, auditoria, sports halls or swimming pools, propagation and reverberation times need to be carefully considered.

The ambient noise levels within an airhouse are largely made up of the noise generated by the inflation system. To a lesser extent noise will also be generated by air leaking through gaps in doors, and through the ground connections, giving rise to a whistling sound. Adjustable vents used for airhouse internal pressure regulation may also produce noise. Rain falling on the membrane can give rise to substantial increases in noise levels.

Fan noise

The components in a fan sound spectrum can be classified as rotational, broadband, vortex and mechanical noise.

Rotational noise This arises from:

Periodic lift forces due to the interaction between the velocity fields of stationary (e.g. scroll or volute outer casing) and moving (e.g. impeller) surfaces.

The pulsation of air as the impeller displaces air in its pathway.

In each case a discrete frequency, the blade passage frequency, J; is emitted, together with possible harmonics, where

f = n N (Hz)

for a fan with number of fan blades, n, and an impeller speed in revolutions per second, N.

It is the air passing through the cut-off section which produces rotational sound; the cut-off is the narrowest dimension between the impeller and the fan housing. The frequency and amplitude of the sound energy emitted depend upon the cut-off geometry and also upon the velocity profile. Smoother profiles generate less sound; fans with a high number of impeller blades have flatter velocity profiles than those with a fewer number.

Broadband and vortex noise This originates from the fluctations in the turbulent air patterns across the fan blades and in the velocity field of the fan intake air and vortex


shedding from the edges of the fan blades. Vortex noise has a frequency characteristic determined by the Strouhal number S, where

/3

f = S 3

for an air flow of velocity v, and having characteristic dimension d; S usually lies in the range 0.15 to 0.20. The resulting sound spectrum due to the turbulence fluctations and the vortex components usually has a broadband character with a maximum level at the frequency defined by the Strouhal number. Research over the years has shown that the turbulence power sound level increases as the sixth power law of velocity. Turbulent intake conditions can cause fan sound levels to increase as much as 10dB.

Mechanical noise Discrete and broadband frequency components can be emitted from fan bearings, belt drives and electric motors. For this reason, special care should be taken over the design and installation of the fan assembly taken as a whole. Fan noise will be radiated through the air inlet, the air discharge and the vibrating fan casing itself.

Croome 3 shows that:

(a) The higher harmonics of discrete frequency sound may be transmitted through the system.

(b) The selection of the drive components is as important as that of the fan.

(c) The nature and level of the sound spectrum is very sensitive to fan speed change.

Fan selection should be made considering the aerodynamic and acoustic specification, besides the more practical considerations of space requirements. The aerodynamic and sound performances of fans are related. The lowest sound levels occur at the maximum fan efficiencies.

Axial and backward-curved bladed centrifugal fans show a distinct minimum sound level near the opt imum air flow condition; this minimum does not occur for forward-curved bladed centrifugal fans. The sound levels of the axial flow fans are a little higher than that of the backward- curve centrifugal fans; in practice, this is partly compensated for by the extra low frequency ( < 300 Hz) attenuation required by centrifugal fans although less is required at higher frequencies (> 300 Hz).

422 Derek J. Croome

If the size, speed and number of impeller blades of an axial flow and a centrifugal fan are the same, the sound spectra of both types will be similar at low frequencies, but the axial fan will probably show more high- frequency sound content. For the same air flow rate and pressure requirements the centrifugal fan will be more likely to have a larger impeller diameter and run at a lower speed than an axial type selected for the same duty, hence the fundamental frequency is usually lower for a centrifugal fan than for its axial counterpart. Fan frequencies can resonate if, in the case of a duct length, l, closed at both ends,

n c f = 2 / for n = 1,2, 3 , . . .

or, if the duct is open at one end,

(2n - 1)c .]g- 4l

where c is the velocity of sound. This is, m principle, just the same as the production of resonant frequencies in organ pipes or in the airways of woodwind and brass instruments.

Musicians use mutes to alter the tone quality of their instruments (i.e. by harmonic damping); they produce various frequencies by opening and closing various lengths of their instruments by valves or keys. In air conditioning, designers wish to subdue sound, rather than create it, by altering the geometry of the ductwork system by absorbing sound using absorbent linings or attenuators by using resonance filters such as a Helmholtz resonator.

Eck 4 derived the following expression for the sound intensity level produced by a fan:

L l = 1 0 1 o g K~bO - 1 ~-v 3+"

where ~b is the flow coefficient, ~ is the pressure coefficient, q is the fan efficiency, v is the average air velocity of the air flow in the fan, K is a constant and the power, n, varies from 1'5 to 4; both n and K are determined by measurement.

If the manufacturer 's measured sound levels are not available, then the overall sound power level, Lw, at the fan inlet or outlet can be estimated f r o m ( d B r e l 0 12W)

L,. = 67 + 10log P + 101ogp (21)

Acoustic design jor . f lex ib le membrane structures 423

o r

L w = 40 + 10 log Q + 20 logp (22)

or

Lw = 105 + 20 log P - 10 log Q (23)

where Q is the air volume flow rate (m3/s), P is t he r a t ed motor power (kW) and p is the fan static pressure (Pa). These calculated values apply to fans operating at their opt imum working point.

The sound power level (Lw) of the fan in the Bath University Airhouse can be calculated using eqns (21) to (23), thus

L w = 6 7 + 10log 3 + 10log 350 = 97.2dB

o r

o r

L w = 40 + 10 log 4.75 + 20 log 350 = 97"7 dB

L w = 105 + 2 0 1 o g 3 - 101og4.75 = 107.8dB

where fan power P = 3 kW, fan static pressure p = 350 Pa and fan flow rate Q = 4.75 m3/s. Since Q and p were measured, L w = 97.7 dB will be adopted for the theoretical design value.

The sound pressure level (Lp) is estimated using the standard equation 4) Lp = Lw + 10 log + ~ (24)

for directivity factor Q, distance from source r, room constant R = S~/(1 - ~ ) , for total surface area S and average sound absorption coefficient ~. The term (Q/4rcr 2) represents the direct sound field and (4/R) is the reverberant sound field.

For the airhouse the average absorption coefficient is

-- Sm°~m + SeO~ e

S m ~- S e

for area of membrane S,, = 3400 m 2, area of earth S e = 2450 m 2, sound absorption coefficient for membrane at 500 Hz is ~,, = 0.064 (using eqn (3)) and for earth ae = 0"15 at 500 Hz (Evans and BazleyS), ~ = 0.085 and room constant R = 636. The effect of the fan noise can be explored using eqn (24) and the results are shown in Table 5 ; a comparison is also made with the measurements taken by Bellew,~ which are also shown in Fig. 12.

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Acoustic design for flexible "membrane structures 425

T A B L E 5 ComParison of Calculated and Measured Values for Fan Sound Distribution in Bath

University Airhouse

Sound pressure level (dB)

Calculated Measured (eqn (24)) (see Fig. 12)

Fan power level 83 97.5 83 (L., (dB)) (measured) (estimated (eqn (22))

Distance from source (m) r = 1 72'3-78"1 86.5 (Q = 1)-92"3 (Q =4) 72-83

2 72-3 86"5 72 4 67.2 81 "4 70 8 63" 1 77.7 69

16 61.7 75.9 66

The sound attenuation varies from 5.8 dB per doubling of distance in the near direct field to 1.8 dB per doubling of distance at 16 m when the effect of the reverberant field becomes more important. The overall at tenuation rate is 1 dB per metre.

When the direct field (Q/4nr 2) equals the reverberant field (4/R), the free field radius is given by

r = 0 . 1 4 x / ~ (25)

When Q = 1, r = 3.53 m and when Q = 4, r = 7"06 m, and it can be seen that the calculated and the measured results support these estimates.

In general, theory and measurement are within 6 dB if the correct fan power level is known. Equations (21) to (23) tend to overestimate fan sound power. The conversion of sound power level to sound pressure level includes several factors which will not be accurately known; in particular, the directivity and t h e sound absorption coefficients. The distribution also is affected by focusing and Bellew 1 shows a range of results which demonstrates the effect of non-uniform sound distribution and frequency (see Table 6).

The importance of knowing the fan sound spectrum is shown in Table 7. For centrifugal fans most of the sound energy is in the low frequencies ( < 5 0 0 H z ) ; axial flow fans emit their sound at higher

426 Derek J. Croome

TABLE 6 Sound Propagation in the Bath University

Airhouse (Bellew ~)

Frequency (Hz) dB/douhling distance

250 2 2.5 500 4

1 000 4 4-5 2 000 4 45 4 000 5 8 000 6

frequencies (700-2000Hz). At distances beyond the free field radius absorptive treatment is effective and, since membranes can be tuned as low frequency absorbers, flexible structures offer a good opportunity for soaking up sound.

Most of the distance attenuation takes place in the first 35 m. The fan has a predominantly low frequency broadband emission and, at 80 Hz, exceeds 70dB. Care has to be taken with regard to discrete frequencies which may be emitted at the fundamental and harmonic blade passage frequencies. In this case, the fan operates at a speed of 400 rpm, hence the fundamental is 6"6 Hz and harmonics occur at n = 1, 2, 3 , . . . times this. The fan in the Bath University Airhouse meets this noise criterion, NR61, and thus, only complies with light industrial use, but plenum attenuators could be designed and installed on the fan outlet to meet the acoustic requirements for office use.

Because sound signals can be propagated very easily around the inside of a lightweight structure, great care has to be taken in setting damper

TABLE 7 Centrifugal Fan Characteristics for Bath University Airhouse

( Bellew i )

Position Sound pressure level measurements (dB)

250 H= 500 Hz 1 000 Hz 2 000 Hz

Fan outlet 68 65 58 54 Near tin (0.5m) 55 60 50 58 47 56 43 55 3 5 m a w a y 50 52 46 50 48 52 46 48 6 8 m a w a y 49 50 45 55 44 51 39 44

Acoustic design Jbr flexible membrane structures 427

positions in air flow systems, otherwise intense directional high frequency 'whistles' will occur; evidence of this is supplied by Bellew.

Rain noise

Concern is often expressed but without direct experience about the question of rain noise. Patterns of rainfall differ in intensity and display large variations within minutes. Storms very rarely last for hours. Even in traditional buildings rain noise is accepted as part of the day-to-day weather variations even though it can be heard if seated near windows and the wind blows the rain against the glass. Bellew ~ recorded four sound spectra in the Bath University Airhouse in a l-min period during one storm.

Two samples produced overall sound levels of over 90 dBA; when the rain slackened the levels fell to 71 dBA and 61 dBA, respectively.

The frequency content also varied. Intense rain can product very high sound levels in the low frequency range (20-200 Hz) and the very high frequency range (1000-20 000 Hz) even beyond the normal range of hearing. At another moment intense rain will produce high sound levels from 20 10000Hz. Less intense rain gave sound emission either in the low frequency ( < 500 Hz) or mid-frequency ( < 2000 Hz) ranges.

Normally this would not be a problem because rain is very intermittent except in monsoon tropical climates. The effect could be reduced by using suspended absorbents to form a roof cavity to soak up the sound. At such times the weather would be dull so artificial lighting would be used anyway. For townships built under membrane roofs the scale and the landscaping will diffuse and attenuate the rain noise effect at ground level; besides people will be able to work inside buildings within the covered township.

Speech

Bellew I conducted some pilot studies on speech communication in the Bath University Airhouse using ten subjects listening to prescribed word lists. The best intelligibility score was 50 per cent for a source-listener distance of 10 m but, beyond this, communication fell off rapidly. Normal recommended intelligibility scores are a minimum of 70 per cent for good communication. The r61e of masking reflections needs to be studied in more detail.

428 Derek J. Croome

Music

Because single membranes display low absorption which decreases even further at high frequencies, stringed instruments show a good tonal response because the structure responds to the higher harmonics which these instruments exhibit. As in the case of speech, the source-listener position is critical but can be aided by the use of suspended sound reflectors.

REVERBERATION TIME CHARACTERISTICS OF THE BATH UNIVERSITY AIRHOUSE

The reverberation time defines the time for the sound to decay to a millionth of its value when the sound is switched off and is an approximate guide to the appropriateness of the space for speech or music. Speech requires a quick decay, so that successive consonants stand out, whereas music needs the musical signals to merge with one another to some degree and to allow wide dynamic and tonal ranges for expression. The general formula used to calculate reverberation time (T) is due to Sabine:

0.16V T = z s ~ S (26)

for volume V(m3), surface areas S(mZ), each with sound absorption coefficient, ~. This formula arises by solving the sound decay equation at a surface

d 5 - S ~

for sound energy density, e, and sound intensity, ec/4. Thus,

,L: ~: = J o 4 dt

where E T = 10 6• m. The assumptions made are that sound energy is uniformly distributed throughout the space; the source gives omnidirec- tional emission; attenuation takes place at the boundaries only; and there is no frequency dependence. Even if the source is uniform the other assumptions are not valid in the airhouse, for the reasons discussed earlier.

An empirical formula given by Stephens and Bate 9 is

T = r(0"012V 1'3 + 0.1070) (27)


where r = 4 for speech r = 5 for orchestral music r = 6 for choir

For the airhouse V = 15 000m 3, hence

T = 1.6 s for speech T = 2.0 s for orchestral music T = 2-4 s for choral music

Any formulation involving 0~ is frequency dependent and so the reverberation time has to be calculated at each frequency. Subjectively, more reverberation is required at low frequencies ( < 500Hz) when listening to music if a warm sonorous sound is to be perceived so that the calcula ted value of T = 2 s for orchestral music would gradually be increased to T = 2.3 to 2.5 s at 50 Hz to give a 'bass tail'.

The sound absorption per cubic metre unit volume of air is 0.003 at 1000 Hz, 0.007 at 2000 Hz and 0-02 at 4000 Hz, so for the airhouse this is 45 (1000 Hz), 105 (2000 Hz) and 300 (4000 Hz) Sabine absorption units, respectively. Depression of the higher frequencies can dull the tone in string music, where brilliance is required.

Sound quality is governed by many more factors than reverberation time and this is discussed by Cremer and M/iller, 2 Jordan 6 and Croome. 3 For comparison purposes reverberation time measurements were made by Bellew 1 in the Bath University Airhouse and the significance of these will now be discussed.

For calculation the Sabine equation (eqn (26)) can be applied to the airhouse:

0.16V T -

SmO~ m q- Se~ e

where V = 15 000 m 3 S,, = membrane surface area = 3400 m 2 S e = earth ground surface area = 2450 m 2 ~m = membrane absorpt ion coefficient (calculated using eqn (3)) c~ e = ground absorpt ion coefficient (using values given by Evans

and Bazley 5 for gravel moist soil pounded to give a firm surface)

= 0.1 (125 250 Hz), 0.15 (500 Hz), 0.25 (1000 Hz), 0.4 (2000 Hz), 0-45 (4000 Hz)

Table 8 lists the calculated and measured values.

430 Derek J. Croome

TABLE 8 Compar i son of Calculated and Measured (Bellew ~) Values of Reverberation Time for Bath University Airhouse: Figures Apply to the Airhouse When

Empty

Frequency Re~,erberation times (s)

(H:) ( 'alculated :kleasured

("entreline Edge

125 1.16 2-0 2"5 1.9 2"5 250 2-42 2.2 3.0 1.9 2.7 500 4.08 3"5 4.2 2.0 3.0

I 000 3-06 3.9 4.0 2.1 3.0 2000 2.44 2.5 3.1 2"2 3.1 4000 2.19 2"0 2-2 1.8 2-6

The trend towards higher reverberation times at 500 Hz and 1000 Hz is evident in both sets of results. As expected, the measurements show that there is much variation in the sound field. In the centre, theory and practice agree reasonably well except at 125 Hz and 1000 Hz. Around the edge of the airhouse the reverberant field is more constant and the effects of curvature are less marked. Table 9 shows a list of design reverberation times for some different uses in a similar volume (15 000 m 3) to the Bath University Airhouse.

Clearly, for speech, the airhouse, when empty, is too reverberant. In

Typical TABLE 9

Reverberation Times at 500Hz for a Building of 15000m 3 with a Variety of Uses

Use Reverberation time (s) at 500 H: j b r a {~olume ~[ 15 O00 m 3

Television studio 0.7 Speech 1-0 1.3 Opera 1.6 Concert studio 1.8 Amplified music 2-0 2.2 Orchestral music 2.2 2-6 Choral, organ music 2.3 3.0


practice, the audience will provide sound absorption. As a general guide it is reckoned that for speech it is necessary to have 3.5 m 3 per seat and for music 7.5m 3 per seat. In the case of the airhouse this would mean audiences of 4286 people listening to speech and 2000 listening to music. The effect of this on the reverberation time can be ascertained using audience absorption values per person of 0.25 (125 Hz), 0.4 (250 Hz), 0.55 (500Hz), 0.65 (1000Hz, 2000Hz) and 0-6 (4000Hz). At 500Hz, for example:

Speech'

T-- (0.16 × 15000) = 0.82s (3400 x 0.064)+(2450 x 0.15)+(4286 × 0.55)

Music (0.16 x 15 000)

T = = 1.42s (3400 × 0.064) + (2450 x 0.15) + (2000 x 0.55)

These values are lower than those recommended so the audience will need to be reduced or some form of suspended reflectors will be necessary. In high and long spaces the use of reflectors will be necessary anyway to keep the delay time within the value of 10-20 ms recommended for speech and music, respectively.

In regular spaces the sound decay curve has a constant slope, but near the centre of the airhouse the decay curves had double slopes, especially at 500 Hz and 1000 Hz (see Fig. 13). The centre of the airhouse has a longer reverberation time at these frequencies than nearer the edge (see Table 8), so in effect the airhouse is reacting acoustically like two connected spaces with different reverberation times. Some effect of flutter echo may also be contributing to the second part of the decay pattern. Focusing of sound energy along the centre of the airhouse is probably responsible for the high reverberation times in this region.

100 -

~ 0O

IOO0 MI ~'t~0 N#

Double slope sound decay curves in Bath University Airhouse near centre (Bellew~).

2$0H I 500N I

Fig. 13.

432 Derek J. Croome

i I ~$0 H i SOOMl ~ O O H I 4000 HJ

soo H~ +O00 H =000 ~x *ooo H I I 10~0 M i

C E lUE O [LAVS (m*$

• q

2SO Nz

7S ~S eS SS 60

oo ~ l i 0 o o Hm ~ooo M+

Fig. 14. Sound impulse echo patterns in Bath University Airhouse (Bellewl). (a) End of Airhouse, (b) centre of Airhouse, (c) near centre~choes occurring at time delays greater

than 60 ms.

Some sound impulse traces were recorded by Bellew, 1 as shown in Fig. 14. The presence of strong reflections can be seen in most of the traces, particularly in the mid-frequencies and near the centre, thus providing supporting evidence for the higher reverberation times in these zones. In some cases these reflections exceed a time delay of 50 ms and will be perceived as echoes, e.g. at 2000 Hz there is an echo arriving 0.6 s after the pulse has ceased. In sports halls constructed from lightweight fabrics several people have experienced a loss of location because there is a confusion between echo signals and the succeeding primary sound signal.

The methods of correcting these acoustical faults in lightweight structures have been described earlier.

R E F E R E N C E S

1. Bellew, P. J., A Survey of the Acoustic Conditions in the Airhouse at Bath University, Final Year Undergraduate Thesis, School of Architecture and Building Engineering, The University of Bath, 1981.


2. Cremer, L. and Miiller, H. A., Principles and applications of room acoustics, Vols 1 and 2, trans. T. J. Schultz, Applied Science, London, 1982.

3. Croome, D. J., Noise, buildings andpeople, Pergamon, Oxford, 1977. 4. Eck, B., Fans, Pergamon, Oxford, 1973. 5. Evans, E. J. and Bazley, E. N., Sound absorbing materials, HMSO, London,

1960. 6. Jordan, V. L., Acousticaldesign of concert halls and theatres, Applied Science,

London, 1980. 7. Kut~truff, H., Room acoustics, Applied Science, London, 1973. 8. Moulder, R. and Merrill, J., Acoustical properties of glass fiber roof fabrics,

104th Meeting of Acoustical Society of America, Orlando, Florida, USA, 1 lth November, 1982.

9. Stephens, R. W.B. and Bate, A.E., Acoustics and vibrational physics, Arnold, London, 1966.

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Acoustic design for flexible membrane structures