C H A R L E S M . S A L T E R A S S O C I A T E S

A C O U S T I C S A R C H I T E C T U R E E N G I N E E R I N G T H E E N V I R O N M E N T

Wave Frequency Sound Pressure and Sound Pressure Level Predicting Sound

Pressure Levels from Multiple Sources Directivity Diffuse Sound Fields The

Inverse Square Law

A sound wave is a physical disturbance o f molecules w i t h i n a med iumai r ,

water, or sol idthat can be detected by a listener. M o s t sound waves result

f r o m a v ibra t ing object . L o o k around and y o u ' l l see countless objects i n a

state o f v ib ra t ion : the w i n d o w s i n your house w h e n a t r u c k drives by, a g u i -

tar w h e n its strings are p lucked , or tree branches i n the w i n d . Each o f these

are examples o f a sound source. These di f ferent waves combine and reach

a listener via numerous direct and ind i rec t pathways.The listener's inner ear

contains organs that vibrate i n response to these molecular disturbances,

conver t ing the vibrat ions in to changing electrical potentials that are sensed

by the b r a i n a l l o w i n g the p h e n o m e n o n o f hear ing to occur.

Acoust ical analysis involves n o t on ly the sound source bu t also w h o

is hear ing i t (receiver) and everyth ing i n be tween (the path). T h e path is

made up o f the env i ronment encompassing b o t h sound source and receiv-

er. T h e m e d i u m o f transmission can either be air, or a c o m b i n a t i o n o f

mediums, i n v o l v i n g a conversion to v ib ra t ion and then back to sound,

t h rough solid objects such as walls and f loors . Figure 2.1 shows an exam-

ple o f the chain o f events f r o m sound source to listener and a generalized

source-path-receiver mode l .

2 8 A c o u s t i c s

Figure 2.1 (top) A generalized

source-path-receiver m o d e l . T h e

source is an en t i ty that causes

acousl:ical v i b r a t i o n . T h e path is the

env i ronmen ta l con tex t and the

t rans format iona l aspects o f the

m e d i u m . T h e receiver can refer to a

h u m a n listener or a m i c r o p h o n e .

(bottom) An example o f t h e source-

path-receiver m o d e l . T h e cuxles

indicate sound radia t ion; the i r da rk -

ness indicates relative intensity. A

listener (receiver) is l i s t en ing to

music from a record player; this is a

desired sound source. I n an a d j o i n -

i n g u t i l i t y r o o m , a machine emits

sound and inf rasonic v i b r a t i o n ; this

is a noise sound source. T h e t w o

rooms and the i r surfaces (path)

t r ans fo rm the acoustical v i b r a t i o n

from the sources before they reach

the Ustener.The sound f r o m the

loudspeaker w i l l reach the ears o f

the listener v ia a direct path and

ind i rec t paths f r o m ref lect ions o f f o f

walls; the latter is t e r m e d reverberation.

T h e mach ine is heard and f e l t

t h r o u g h the w a l l as a result o f .(owi/rf

transmission (the w a l l i t se l f becomes

a v i b r a t i n g source) and possibly due

to sound leakage t h r o u g h cracks i n

the cons t ruc t ion .

Sound source Path Receiver

T h e percept ion o f a listener can be in f luenced by the treatment o f

either the path or the source. For instance, we can enhance the m t e l l i g i -

b i h t y o f speech m a conference r o o m by electronically a m p l i f y i n g the spo-

ken voice, or the sound ou tpu t f r o m a power plant can be reduced to l i m i t

the disturbance m a communi ty . N o t e the dis t inct ion m these examples

between the spoken voice and the sound sources. T h e spoken voice is

desirable, w h i l e sound f r o m a power plant is not ; w e refer to undesirable

sound as noise.

Figure 2.2 Compress ion and

rarefac t ion o f air molecules at f ive

discrete m o m e n t s o f t ime . T h e " + "

indicates compression (an increase

i n pressure) and the " - " indicates

rarefact ion (a decrease i n pressure).

Th i s represents a single cycle o f

pressure va r i a t ion .

W a v e F r e q u e n c y

T h e molecular disturbance caused by an acoustic source involves a series

o f h i g h and l o w pressure areas ( termed compression and rarefaction). F i g -

ure 2.2 shows f ive discrete moments o f t ime that comprise a single wave

cycle. A n equivalent i l lustrat ion, indica t ing pressure var ia t ion cont inuously

over t ime, is shown i n Figure 2.3.

A ioundh frequency is def ined i n terms o f t h e number o f wave cycles

that occur d u r i n g one second. T h e u n i t used f o r describing f requency is

hertz (Hz) . For higher frequencies, kilohertz (kHz) is used to indicate the

number o f osciUations times 1,000 that occur w i t h i n a second. For exam-

ple, 1.68 k H z (1.68 X 1000 (ki lo) H z ) is the same f requency as 1,680 H z .

'rPo r i .V.

Time

F u n d a m e n t a l s

Time

I f y o u drop a rock in to the nhddle o f a lake, ripples propagate o u t -

ward f r o m the p o i n t o f contact. These circular ripples are comparable to

sound waves traveling t h rough air. I f y o u count the number o f wave r i p -

ples that pass a single p o i n t o n the lake d u r i n g one second, y o u can calcu-

late the wave's frequency. For example, the f requency o f the red wave i n

Figure 2.4 is f ive times greater than the f requency o f the black wave.

Waves that have a repeated pat tern o f oscil lat ion are called periodic

waves. Figures 2.3 and 2.4 show the simplest type o f per iodic wave, the sine

wave. Sine waves (also called "pure tones") have a single constant f r equen-

cy obtainable on ly f r o m electronic devices.

H o w do these frequencies relate to hearing? W h e n the fi-equency is i n

the range o f roughly 20 H z to 20 k H z , the waves are heard as sound waves;

these are termed audio frequencies. H u m a n speech contains frequencies that

He between 200 H z and 5 k H z ; the sound o f an orchestra can contain f r e -

quencies between 25 H z to 13 k H z or even higher. Frequencies be low

20 H z are sensed as v ibra t ion , are not audible to most people, and are t e rmed

infrasonic. Frequencies above 20,000 H z are te rmed ultrasonic.

Figure 2.5 shows the typical f requency range f o r various sound

sources. JNAany situations encountered i n buildings involve a c o m b i n a t i o n

o f b o t h audio and infrasonic frequencies; that is, sound and v ib ra t ion . For

instance, at frequencies up to around 100 H z , such as those produced by a

pipe organ, i t is possible to simultaneously hear sound and feel vibrat ions.

R e a l - w o r l d waves are no t as per iodic as those jus t described; i n fact,

most waves usually conta in a m i x t u r e o f many frequencies. W h i l e a sine

wave is considered technically to be a "s imple" wave, i n actuality, almost all

waves i n nature are "complex ," i n that they conta in m u l t i p l e frequencies.

T h e reason a v i o l i n and a v io la sound dif ferent f r o m each other is because

each has a d i f ferent combina t i on o f frequencies, w h i c h is referred to as the

sound source's spectrum .The in te rac t ion and behavior o f t h e d i f ferent f r e -

quencies w i t h i n a .spectrum can be quite complex , and are i n fact respon-

sible f o r the r i c h palette o f sound colors that we experience daily. U s i n g

the treble and bass tone controls o f a h o m e audio system is an everyday

example o f h o w a sound's spectrum can be changed by selectively empha-

sizing some frequency components and de-emphasizing others.

Figure 2.3 A single cycle (wave-

l eng th per iod) o f a con t i nuous ly

repeating wave (here, a sine wave) is

shown as a con t inuous f u n c t i o n o f

t i m e o n the x axis, w i t h pressure o n

the y axis s h o w n m b o t h posit ive

and negative direct ions f r o m the

center l ine .

T h e speed o f sound t h r o u g h air

depends o n a n u m b e r o f e n v i r o n -

menta l factors such as temperature

and humidi t )^ : a g o o d a p p r o x i m a t i o n

is 344 m/sec (1,128 f t / s e c ) . T h e

speed w i l l vary depend ing o n the

propagat ion m e d i u m ; f o r instance,

the speed o f sound is faster t h r o u g h

water than t h r o u g h air.

Figure 2.4 T w o sine waves w i t h

d i f fe ren t frequencies. T h e red sine

wave has a f requency that is five

times the f requency o f t h e black sine

wave, because there are five

repetit ions o f the wave over the t i m e

span tg - t i .

F u n d a m e n t a l s 3 1

S o u n d P r e s s u r e a n d S o u n d P r e s s u r e L e v e l

T h e concept of sound pressure is basic to an understanding o f sound waves.

Figure 2.3 shows h o w sound pressure represents an increase and decrease

above and be low the atmospheric air pressure w e n o r m a l l y experience. A

var ia t ion i n sound pressure is perceived as a change i n loudness; loudness

is discussed i n Chapter 3.

T h e range o f sound pressures that humans can detect is enormous.

T h e quietest sound a typical y o u n g person can hear is equivalent to

20 micropascals (.00002 pascals), w h i l e the most intense sound that humans

can tolerate is equivalent to a sound pressure o f around 200 pascals (Pa).

Th i s is a change i n magni tude o f 10,000,000 to 1! B y using a part icular

logar i thmic u n i t k n o w n as the decibel (dB) , a w i d e range o f pressure mea-

surements are compressed on to a logar i thmic scale.The dB scale is easy and

convenient to use w h e n describing sound. T h e range o f decibels laiost

c o m m o n l y encountered i n acoustics extends f r o m 0 to 140 d B 0 d B cor-

responding to the threshold o f hearing, and 140 dB corresponding to the

threshold o f pain. W i t h i n these l imi ts is the dynamic range o f the aud i to -

ry systenr. A sound pressure expressed using the dB scale is t e r m e d the

sound pressure level (SPL) and is the most f requent ly used met r ic i n

acoustics. I n order to go f r o m sound pressure to SPL, there are three steps:

Figure 2.6 (top) A noise wave: c o n -

trasting the sine wave, a noise wave

is comple te ly aperiodic .

Figure 2.7 (bottom) A close-up o f

the noise s h o w n i n Figure 2.6.

Figure 2.8 A speech wave o f the

w o r d " l e f t . " N o t e h o w this wave

varies over t ime . T h e "e" p o r t i o n o f

the wave is m o r e p e r i o d i c than the

" f " p o r t i o n , w h i c h is noisy.

Time

(1) convert the sound pressure at successive instantaneous values in to an

average sound pressure over a particular t ime pe r iod ; (2) express this aver-

age value as a ratio to a reference level that is based o n the threshold o f

hearing; and (3) convert to a decibel scale by m u l t i p l y i n g 20 times the l o g -

a r i t h m o f that ratio.Table 2.1 shows comparative sound pressure and sound

pressure level values f o r c o m m o n sound sources.^

P r e d i c t i n g S o u n d P r e s s u r e L e v e l s f r o m M u l t i p l e S o u r c e s

I n many cases, i t is desirable to predic t h o w the sound pressure level w o u l d

change by adding addit ional sound sources. For example, consider the

sound o f a single p u m p i n a mechanical equ ipment r o o m . A n engineer

Technically, sound pressure is a

measure o f acoustic force over a

u n i t area, measured i n newtons per

meter squared ( n e w t o n / m ^ ) . O n e

n e w t o n / m - ^ is equivalent to one

pascal (Pa); it's easier to say " 2

pascals" than "2 newtons per meter

squared." A newton is the a m o u n t o f

force needed to accelerate a mass o f

one k i l o g r a m one me te r per second

per second.

32 A c o u s t i c s

Table 2.1 C o m p a r i s o n o f sound

pressure and d B S P L f o r typ ica l

sound sources.

Sound Sound pressure

pressure (Pa) level (dB) Example sound source

200.0 140 Threshold of pain

20.0 120 N e a r a jet aircraft engine

2.0 100 N e a r a jackhammer

0.2 80 Typical factory

0.02 60 Normal speech level

0.002 40 Q u i e t living r o o m

0.0002 20 Q u i e t recording studio

0.00002 0 Threshold of hearing

T h e mathemat ica l d e f i n i t i o n o f

sound pressure level:

d B S P L = 20 log ( P I / P Q )

W h e r e the value o f is the aver-

age pressure o f the wave, and Pg is

a inbient a tmospher ic pressure

(equivalent to the threshold o f

hear ing) . A n in t e rna t iona l standard

sets Pg to a sound pressure level o f

.00002 n e w t o n s / m 2 . \ )7hen P , is

equal to Pg, the equa t ion w o r k s o u t

to be equal to the standardized re f -

erence level o f 0 d B .

Difference betv/een Add to higher

two sound levels sound level

0 or 1 dB 3 dB

2 or 3 dB 2 dB

4-9 dB 1 dB

10 dB or more 0 dB

Table 2.2 D e c i b e l A d d i t i o n

Newtons? Pascals? Hertz? Decibels?

These scientific units are based on

the names o f p r o m i n e n t figures i n

science. H e r t z honors the 19 th cen-

t u r y scientist H e i n r i c h H e r t z .

N e w t o n s are named after Sir Isaac

N e w t o n , w h o sat under apple trees

and invented di f ferent ia l calculus.

Pascal was a famous French m a t h e -

mat ic ian o f t h e 17 th c e n t u r y . A n d

the decibel is named after Alexander

Graham BeU, the fa ther o f t e l ephony

measures the sound at a reference distance (typically 1 m) and obtains a

level o f 65 dB. T h e engineer wants to k n o w wha t the sound level w o u l d

be i f several more pumps were added i n the r o o m . H o w does an engineer

predict the sound level o f mul t ip l e sound sources? I n our example, adding

an addi t ional p u m p i n the r o o m w o u l d no t double the sound pressure

level; dB values are n o t additive. A simple calculation o f the total resulting

sound pressure level can be made by using the f o l l o w i n g shortcut f o r deci -

be l addi t ion: (1) i f the difference between t w o sound levels is 0 or 1 dB,

add 3 dB to the higher level; (2) i f the difference between t w o sound lev-

els is 2 or 3 dB, add 2 d B to the higher level; (3) i f the difference between

t w o sound levels is 4 to 9 dB, add 1 dB to the higher level; (4) i f the d i f -

ference between t w o sound levels is 10 dB or more, the resuk is the h i g h -

er o f the t w o sources; and (5) to combine more than t w o levels, f irst add

the t w o lowest together according to the above rules; then add the next

t w o lowest levels together u n t i l on ly t w o values are obtained. T h e n the

above rules are apphcable (see Table 2.2).

R e f e r r i n g back to the problem, we have one p u m p measured at

65 dB. T w o pumps w i t h the same level w i l l result i n an addit ional 3 dB (or

68 dB total). For three pumps, the t w o lower sound levels are added togeth-

er: since they are the same level, we get 68 dB + 65 dB, resulting m 70 dB.

For f o u r pumps, 65 dB 4- 65 dB = 68 dB f o r pumps one and t w o ; 65 +

65 d B = 68 dB f o r pumps three and four ; and therefore add 68 4- 68 dB,

w h i c h results m an overall level 71 dB. W i t h five pumps, the total is 72 dB

(71 dB 4- 65 dB) .Thus , five pumps w o u l d be 7 dB louder than one pump.

To combine mul t ip l e sound sources together o f the same intensity,

the f o r m u l a is SPL + 10 l o g ( N ) = Total sound level, where SPL is the

sound level o f one sound and N is the number o f sources. To check our

answer above: 65 + 10 log(5) = 72 dB.

D i r e c t i v i t y

T h e spatial properties o f either a sound source or a receiver at various f r e -

quencies and directions constitute its direct ional pat tern or J/rerf;V/ty.When

a sound source radiates energy evenly i n all directions i t is called o m n i d i -

rectional . Therefore , an omnid i rec t iona l mic rophone w o u l d be equally sen-

F u n d a m e n t a l s 3 3

sitive to sounds f r o m all directions, bu t most sound sources emi t more

power i n some directions than others. A j e t engine, f o r instance, is m u c h

louder o n its exhaust side than o n its intake side. Each f requency that

makes up the sound source w i l l have its o w n direct ivi ty. Figure 2.9 shows

the direct ional pat tern f o r various frequencies emi t t ed by a loudspeaker.

250 Hz 500 Hz

I kHz 8 kHz 16 kHz

T h e lower frequencies are less direct ional than h igher frequencies. I n gen-

eral, w h e n a wavelength o f a sound is larger than the source generating i t ,

the sound pattern has an omnid i rec t iona l characteristic.

D i f f u s e S o u n d F i e l d s

Direc t sound is the sound wave that reaches the listener via a direct path,

w i t h o u t having bounced o f f a ref lec t ing suiTace. A diffuse sound field, on the

other hand, refers to the energy f r o m a sound source that reaches the l i s -

tener indirectly, after ref lec t ing o f f su r rounding surfaces. T h e bu i ldup o f

diffuse sound over t ime is k n o w n as reverberation. Reverbera t ion is a c o l -

lec t ion o f t ime-delayed versions o f a sound that have decayed i n intensi ty

over t ime as they arrive at the listener. A representation o f the reverbera-

t i o n process is shown i n Figure 2.10.

W h i l e reverberation is most of ten heard i n enclosed spaces, sound

reflections also occur i n ou tdoor settings. O n l y i n anechoic chambers or i n

atypical environmental locations such as on a m o u n t a i n summi t is sound

ever free o f reflections. This is the d e f i n i t i o n o f z f r e e sound field,"a m e d i -

u m where on ly the direct sound reaches the receiver." I n most rooms, the

direct and t ime delayed sounds arrive so qu i ck ly i n succession that they are

perceived as one sound source, a r r i v ing f r o m a single loca t ion def ined by

the direct sound. However , i f the ref lec t ion arrives late enough i n t ime and

has a signif icantly h igh ampli tude, i t is heard separately as an echo.

Figure 2.9 D i r e c t i o n a l propert ies o f

a loudspeaker. Each p l o t shows the

d i r ec t iv i ty f o r a d i f fe ren t f requency.

N o t e h o w the sound becomes m o r e

direct ional w i t h increasing frequency.

Environmental context

Source

Direct Early sound reflections

Listener

Late reflections (reverberation)

Time

Figure 2.10 (top) A s i m p l i f i e d p l o t o f

a direct sound (blue) and t w o early

reflect ions (red) f r o m a sound source

to a hstener. (bottom) R e f l e c t o g r a m

s h o w i n g direct sound (blue), early

reflect ions (red), and reverberat ion

(g reen) .The early and late ref lec-

tions taken together const i tu te the

diffuse sound field.

34 A c o u s t i c s

Figure 2.11 T h i s impulse response

was obta ined b y p o p p i n g a ba l l oon

i n a r o o m and r eco rd ing the results.

T h e arrows indicate s igni f icant early

ref lect ions.

Figure 2.11 shows an iiTipulse response o f a r o o m , obtained by record-

ine a ba l loon pop. A r o o m impulse response is a graphic representation o f

the m o m e n t - t o - m o m e n t variat ion o f sound pressure m a diffuse f ie ld . T h e

r o o m impulse response is equivalent to the reflectogram shown at the b o t -

t o m o f Figure 2.10. T w o possibly significant early reflecdons that m i g h t be

heard as echoes are indicated by arrows i n Figure 2 .11 . Chapter 6 treats the

topics o f reverberation, echoes, and difliise sound fields m greater depth.

T h e I n v e r s e S q u a r e Lavw

T h e inverse square law expresses the decrease m sound pressure as a f u n c -

t i o n o f distance. Each doubhng o f distance f r o m a reference p o i n t translates

in to a 6 dB loss m sound pressure level as shown m Figure 2.12.

T h e inverse square law p r i m a r i l y pertains to p o i n t sound sources

ou t -o f -doors . Examples approximat ing po in t sound sources include w i n -

d o w air condit ioners and loudspeakers. A l ine source o n the other hand

radiates sound cy lmdr i ca l l y U n l i k e the p o i n t source, the sound pressure

level f o r a l ine source w i l l be reduced by 3 dB f o r every d o u b l i n g o f dis-

tance. Water passing th rough a pipe approximates a l ine source.

The area of the

wavefront is 4 times

greater at d, (2m)

Sound

source

Area of

the wavefront

at d| ( Im)

72 dB 66 dB

Figure 2.12 T h e inverse square law.

Because the area o f the wave is f o u r

t imes as large f o r each d o u b h n g o f

distance, there is a 6 d B loss.

T h e inverse square law can be very useful fo r estimating the f a l l - o f f i n

direct sound level fi-om an outdoor source. However, f o r a sound source m a

reverberant r o o m , the inverse square law does not apply This is because the

reverberation contributes to the overall level; the f a l l - o f f m the direct sound

level is compensated fo r by reverberant energy that builds up w i t h i n a r o o m .

F u n d a m e n t a l s 3 5

C o n c l u s i o n

I n this chapter, the fundamenta l concepts o f acoustics were in t roduced: f r e -

quency, sound pressure level, spectrum, directivity, and reverberation. A l l o f

these concepts are measurable i n a physical sense, bu t Chapter 3, "Psycho-

acoustics and Hear ing , " covers h o w we interpret these fundamenta l c o n -

cepts. Acoust ical measurements make up a large part o f the engineer ing

efforts i n acoustics. Chapter 4 discusses techniques used f o r measuring the

frequency and ampli tude o f noise.

S o u n d Power Level

(dB) = l O l o g i o ( W , / W , | )

W h e r e W I is the p o w e r i n watts o f

the sound source, and W Q is the r e f -

erence p o w e r level o f 1 p i cowa t t .

Sound intensity (I) refers to the rate

o f f l o w o f sound energy per u n i t

area in a specified d i r ec t ion ; i t rs

therefore a measurement o f n o t o n l y

sound pressure b u t molecu la r air

par t ic le velocit)^. As w i t h SPL, the

sound intensity lettel is measured as a

ra t io to a reference quanti ty. I n a /fee

sotind fteld, an open field, or o ther

env i ronmenta l con tex t w h e r e

ref lected sound is e f fec t ive ly n o t

present, the values obta ined f o r SPL

and sound in tensi t ) ' level arc the

same:

Sound in tens i ty level

d B = 10 l o g , , , ( I , / l o )

W h e r e I | is the p o w e r measured i n

wat ts /m'^ and In is a reference value

o f 10- '2 watts/m2.

Notes

1. I t IS possible to refer to the soutid

power ( W ) o f a source, independen t

o f the distance and d i r e c t i v i t y o f the

source, u n l i k e the sound pressure

level . A sound source radiates sound

waves whose total p o w e r can be

measured i n ivatts, a standard scien-

t i f i c u n i t f o r measur ing energ)^,

w o r k , o r the quan t i ty o f heat. L i k e

sound pressure level , the sound

power level is expressed m a t h e m a t i -

cally as a d B ra t io to a reference

level . I n this case, the reference is

10"'2 watts (1 p icowat t ) :

The Auditory Mechanism Perceptual Interpretation of Physical Cues Pitch

Loudness Timbre and Spatial Location The Precedence Effect Psychoacoustic

Measures

H U M A N hearing can be separated in to physiological and perceptual aspects.

T h e physiology o f hearing refers to aspects o f t h e audi tory mechanism that

respond directly to acoustical events, w h i l e percept ion refers to processing

o f acoustic events by the brain. T h e connect ion between physical measure-

ments o f sound, the percept ion o f the Hstener, and legal or scientific stan-

dards is illustrated i n Figure 3 . 1 .

T h e A u d i t o r y I V I e c h a n i s m

TraditionaUy, the audi tory mechanism is subdivided in to the outer, middle ,

and inner ear. Figure 3.2 and this text provide a t h u m b n a i l sketch o f the

audi tory mechanism, along w i t h a descript ion o f their f u n c t i o n . Sound first

enters the audi tory mechanism via the pinna (the visible p o r t i o n o f the

outer ear) .The pinna acts as a filter whose frequency response depends o n

the incidence angle o f sound. Because o f this, the pinna is considered to

f u n c t i o n as a cue to audi tory localization. FoUowing the pinna, i n c o m i n g

sound is t ransformed by the efliects o f t h e meatus (or "ear canal") .The mea-

tus can be approximated by a tube 6 m m (0.2 in.) i n diameter and 27 m m

(1.0 in.) l ong , w i t h a resonant frequency o f around 3.5 k H z .

T h e end o f the ear canal marks the beg inn ing o f the midd l e ear,

w h i c h consists o f the eardrum and the ossicles (the smaH bones popular ly

3 8 A c o u s t i c s

Sound source

Listener

(ptiysiology, perception)

+

l^easurement

device

Data relating perceptual

and physical measures

Acoustical & noise

control standards

Figure 3 . i T h e relat ionship be tween

object ive physical measures and

subjective perceptual measures form

the basis for many acoustical and

noise c o n t r o l standards.

t e rmed the "hammer -a i i v i l - s t i r rup" ) . Sound is t ransformed at the midd le

ear f r o m acoustical energy at the eardrum to mechanical energy at the ossi-

cles. T h e ossicles convert the mechanical energy in to f l u i d pressure w i t h i n

the inner ear (the coMed) via m o t i o n at the oval w i n d o w . T h e f l u i d pres-

sure causes f requency-dependent v ib ra t ion patterns along the approxi -

mately 30 m m (1.0 in.) l o n g basilar membrane w i t h i n the inner ear.These

v ib ra t i on patterns cause numerous fibers p r o t r u d i n g f r o m audi tory hair

cells (cilia) to bend at certain locations along the basilar membrane.

H i g h f requency sound activates the basilar membrane near its c o n -

nec t ion beneath the oval w i n d o w . W i t h lower frequencies, the v ib ra t ion

occurs far ther along the membrane. These ciha i n t u r n activate electrical

potentials w i t h i n the neurons o f t h e audi tory system, resulting m aural per-

cept ion and cogn i t ion .

H e a r i n g loss or damage to the hear ing mechanism can be caused by

either b r i e f o r l o n g - t e r m exposure to appropriately h i g h sound levels.

Damage to the hear ing mechanism or to health i n general is t e rmed a

physiological effect o f noise, and can result f r o m b o t h unsafe w o r k c o n d i -

tions and l o u d recreational activities such as Hstening to music t h rough

headphones or f i r i n g guns. T h e hear ing loss that occurs naturally i n aging

is k n o w n as presbycusis.

P e r c e p t u a l I n t e r p r e t a t i o n of P h y s i c a l C u e s

U n d e r cont ro l led condi t ions , a measurement o f a physical aspect o f sound

IS repeatable, a l l owing an accurate p red ic t ion o f its variables. B y contrast,

the measurement o f h u m a n perceptual response to sound is less pre-

dictable, and has a non- lmear relationship to physical measurements. For

these reasons, a d i s t inc t ion is made between acoustics and psychoacoustics.

Psychoacoustics refers to the scientific study o f h u m a n audi tory percep-

tion. T h e non-l inear relationship between physical and psychoacoustical

aspects o f sound can be made by the f o l l o w i n g analogy to cook ing . A chef

can add 1, 1^4, or 4 teaspoons o f oregano to a sauce, bu t the sauce w i t h 4

tea,spoons w i l l n o t taste " f o u r times as spicy," and i t may be impossible to

not ice the difference between a sauce w i t h 1 and 1>'4 teaspoons.Taste is the

perceptual d imension, w h i l e the amount o f spice added to the sauce is the

physical d imension . T h e change i n the physical d imens ion does n o t cor re-

spond to the same propor t iona l change i n the perceptual d imension.

Psychoacoustic studies (col loquial ly referred to as "Hstening tests")

are conducted m order to estabhsh a standardized relationship between

physical and perceptual phenomena, f o r instance, between sound pressure

level and loudness. C a r r y i n g the c o o k i n g analogy fur ther , a gastronomic

exper imen t c o u l d estabhsh the relationship be tween "teaspoons o f

oregano" and "perceived spiciness." A similar procedure is used f o r estab-

l i sh ing relationships be tween physical and perceived magnitudes o f sound.

Table 3.1 identifies equivalent physical and psychoacoustical parameters.

T h e relationship between physical and perceptual parameters have been

incorpora ted i n t o noise cont ro l standards. Studies have investigated the role

o f noise i n d is turb ing sleep; as a consequence, noise cont ro l standards aUow

P s y c h o a c o u s t i c s a n d H e a r i n g 39

Outer Ear Middle Ear Inner Ear

Figure 3.2 O v e r v i e w o f t h e aud i to ry

system. A . p inna; B . meatus; C . ear

d r u m ; D . ossicles; E . oval w i n d o w ; F.

cochlea; G. aud i to ry nerve.

less noise at n igh t than d u r i n g the day. M o s t people have experienced h o w

background sound can inf luence daily activity. Similarly, there are many

documented studies o n h o w w o r k per formance or learn ing can be ad-

versely affected by noise. These are called behavioral effects o f noise, i n

contrast to the physiological noise effects discussed earlier.

P i t c h

Frequency is a measurable quantity, whereas p i t c h refers to the percept ion

o f fi-equency. Pitch is also a t e r m used by musicians to refer to musical

notes; someone w i t h "perfect p i t c h " is skil led at ma t ch ing a p i t c h to an

exact frequency. O n e t e r m c o m m o n to b o t h musicians and acousticians is

the octave. An octave relationship is a f requency in te rva l be tween t w o

sounds whose rat io is 2 .Thus , 100 H z to 200 H z is an octave; as is 31.5 H z

to 63 H z .

P i t ch can be i m p o r t a n t f o r descr ibing certain types o f problems i n

noise con t ro l applications. General ly a noise is most d i s turb ing w h e n i t is

concentrated i n a na r row f requency range; this is t e r m e d tonal noise. T h e

sound f r o m a machine can have a specific p i t c h due to the f requency o f

the motor 's oscil lat ion; fo rced air can whis t le across a ven t .We are all f a m i l -

iar w i t h the h u m o f the ballasts i n a fluorescent l i g h t system. Broadband

noise, conversely, w o u l d be exempl i f i ed by the sound o f distant fleely

flowing t raff ic .

Physical Perceptual

Terminology Terminology

Frequency Pitch

Sound pressure Loudness

level

Spectrum Timbre (tone color)

Table 3. t Physical versus perceptual

t e rmino logy .

L o u d n e s s

Scientif ic tests have de te rmined the relationship be tween sound pressure

level and the percept ion o f loudness. T h e equal loudness contours (also

t e r m e d "F le t che r -Munson curves") i n Figure 3.3 show this relationship.

T h e graph's contours indicate levels i n terms o f phons, w h i c h represent

equal loudness f o r a g iven pure tone SPL referenced to 1 k H z . For

instance, the red dots o n the con tour l ine f o r 40 phons show that 62 d B at

4 0 A c o u s t i c s

Figive 3.3 Equal- loudi iess con tours

for pure tones ( F l e t c h e r - M u n s o n

G r a p h ) . T h e c o n t o u r lines indicate

equal loudness levels (phons) relative

to a 1 k H z frequency. R e f e r to text

f o r discussion o f red dots o n the

40 p h o n c o n t o u r l ine .

120

100

80

60

40

20

20 100 500 Ik

Frequency (Hz)

5 k I Ok

T h e equivalence be tween p i t c h and

f requency becomes m o r e c o m p l i c a t -

ed w i t h real sound sources. For

example, musicians c o m m o n l y

modu la te f r equency over t i m e using

a t echn ique k n o w n as v ib ra to .

A l t h o u g h the f r equency is var ied as

m u c h as a semitone at a rate o f 5 to

8 H z , a single p i t c h is perceived.

100 H z sounds equally l o u d as 40 d B at 1 k H z , and 50 dB at 10 k H z . T h e

f requency w e i g h t i n g filters bu i l t i n to sound level meters described i n

Chapter 4 physically approximate these contours.

N o t surprisingly, the contours that exhib i t max ima l sensitivity are at

those frequencies associated w i t h speech (approximately 200 H z to 5 k H z ) .

A t m e d i u m and h i g h sound levels, the contours are relatively linear, w h i l e

at lower levels, the contours indicate that sensitivity to l o w frequencies is

less than at h i g h frequencies. Thus , the relationship between physical and

perceptual scales is dependent o n b o t h f requency and sound pressure level.

A n o t h e r measurement o f loudness is the sone scale. A sound w i t h a l o u d -

ness o f 40 phons is equal to 1 sone. This is an ar i thmet ic scale such that a

d o u b l i n g i n sones is equivalent to a doub l ing o f loudness. T h e f o r m u l a f o r

relating sones and phons is: sones = 2(pl"'"^ ~ 4 ) / l 0 ^

For c o m m u n i t y noise assessment, certain sound sources that are considered

to be noisy by one group o f people may not be a p rob lem f o r another

group. A general procedure i n such assessments is that the average person's

level o f annoyance needs to be considered. A b o u t 10 percent o f any p o p -

u la t ion can be expected to object to any noise no t o f their o w n mak ing .

Th i s group is referred to as hypersensitive. A b o u t 25 percent are practical-

ly imperturbable . This group is insensitive to noise. T h e remain ing t w o -

thirds group are considered people w h o have wha t is called n o r m a l sensi-

t ivi ty . Some people w i l l object to certain noises t h rough association; f o r

example, the fear o f having an aircraft crash in to one's house can motivate

ob jec t ion to aircraft sound, w h i l e another type o f sound at the same sound

level may no t be perceived as dis turbing.

P s y c h o a c o u s t i c s a n d H e a r i n g 41

One type o f psychoacoustic measure is k n o w n as A just noticeable dijfer-

ence ( JND) . A n example o f a J N D as applied to environmental acoustics is i n

Table 3.2, w h i c h shows the expected response to an increase i n noise level.

T i m b r e a n d S p a t i a l L o c a t i o n

T h e spectrum o f a sound source is largely responsible f o r the perceptual

quahty of timbre, or " tone color." T i m b r e is sometimes def ined i n terms o f

wha t i t is not , f o r example, "the qual i ty o f sound that distinguishes i t from

other sounds o f t h e same p i t c h and loudness." O u r abil i ty to discriminate

between different timbres is very comphcated and n o t fuUy understood, bu t

the m a i n cues seem to involve the change i n a sound's spectrum over t ime.

Spatial loca t ion is also an impor t an t perceptual qual i ty o f sound. T h e

audible difference i n level between the ears as the loca t ion o f a sound

moves relative to a listener is t e rmed an interaural level difference, and is the

same cue manipula ted by a stereo sound system. For instance, i f y o u snap

you r fingers to the r i g h t o f y o u r head, the level w i l l be louder at the r i g h t

ear than at the le f t ear. H i g h frequencies above 1.5 k H z are shielded fi-om

the opposite ear by the head. A n o t h e r cue f o r spatial hear ing is the inter-

aural time difference. T h e wave reaches the r i g h t ear before the le f t ear, since

the path length to that ear is shorter .This t ime difference cue is most effec-

tive f o r frequencies be low 1.5 k H z .

Besides level and t ime differences, another cue f o r local izat ion is the

spectral m o d i f i c a t i o n caused by the outer ears (the pinnae). For every

sound source posi t ion relative to a listener, the pinnae cause a un ique spec-

tral m o d i f i c a t i o n that acts as an acoustic signature, as s h o w n i n Figure 3.4.

These spectral modi f ica t ions are especially i m p o r t a n t i n perceiving the

u p / d o w n and f r o n t / b a c k locations o f a sound source.

Increase

in noise Expected

level (dB) response

1 Possibly detectable under

laboratory conditions

6 Some individual com-

ment and reaction is

expected but no group

action is likely

10 Perceived as twice as

loud

20 Perceived as four times

as loud

Table 3.2 Expec ted response to

increase i n noise level.

T h e P r e c e d e n c e E f f e c t

T h e precedence effect (also called the "Haas effect") explains an i m p o r t a n t

i n h i b i t o r y mechanism o f the audi tory system that allows one to hear

Front

Figure 3.4 Spectr al m o d i f i c a t i o n

caused b y the pinnae f o r t w o p o s i -

t ions . N o t i c e h o w the sound is

b r i g h t e r i n fi'ont and m o r e attenuat-

ed i n back. Inset: overhead v i e w

s h o w i n g sound source posi t ions.

-SO

Ik 2k 4k 6k 8k I Ok

Frequency (Hz)

12k 14k 16k

42 A c o u s t i c s

sounds i n the presence o f reverberation. I t is also i m p o r t a n t f o r under-

standing the disturbance o f speech in t e l l i g ib i l i t y i n rooms. A l t h o u g h w e are

bombarded w i t h mul t ip l e sound reflections i n a reverberant envi ronment ,

our hear ing system interprets the sound as located at one po in t . U p to

about 40 msec, we perceive b o t h sound reflections and the direct sound as

a single, integrated sound source. I n other words, the direct sound takes

precedence over the later sounds.This is also true f o r sound reflections after

about 40 msec, i f the ampl i tude o f t h e reflections is l o w enough. B u t i f the

ampl i tude o f a re f lec t ion is suf l ic ient ly h igh , and occurs after about

40 msec, we hear the ref lec t ion as a separate sound source, or echo, because

the precedence effect no longer operates. This is the same type o f echo

experienced w h e n shout ing i n t o a canyon and the sound re f lec t ion o f f the

walls i n the distance is heard. Echoes can be very dis turbing i f heard dur -

i n g a music per formance or d u r i n g a lecture; as a result, echo m i t i g a t i o n is

an impor t an t part o f r o o m acoustics design.

P s y c h o a c o u s t i c I V I e a s u r e s

M a n y o f the noise cr i ter ia discussed i n this b o o k are based o n psychoa-

coustic measures. I n other words, an attempt is made to relate a physical

measurement o f a quant i ty to a perceptual quantity, i n order to predict

h u m a n response to a given acoustical phenomenon .

Some specific psychoacoustic measures that are c o m m o n l y used are

listed i n Table 3.3. As an example, Figure 3.5 illustrates Noise Cr i t e r i a

( N C ) curves, w h i c h are used f o r relating background noise to the octave

Table 3.3 Re la t ionsh ip be tween

some psychoacoustic measures and

applications.

Psychoacoustic-based measure

Ardculation index (Al)

Speech interference level (SIL)

A-weighted sound levels (dBA)

Noise criteria (NC) curves

Noise criteria-A (MCA) curves

Noise criteria-B (NCB) curves "balanced noise criterion"

Preferred noise criteria (PNC)

Room criteria (RC)

Perceived noise level (PNL)

Description & Application

Estimate of speech intelligibility in noisy contexts

Simplified Al method

dB levels adjusted for a particular equal loudness contour Widely used as "general measure," hearing conservation (OSHA), and community noise ordinances

Frequency-based value used to describe maximum allowable background noise, used for continuous (as opposed to time-varying) noise

Like N C , but curves allow more low-frequency noise

An improved version of N C curves, accounting for speech interference level by HVAC systems

Like N C , but curves adjusted for characterizing a "blander" background noise

Like N C , but curves extend to lower frequencies; designed to be more sensitive to "rumble" and "hissiness" from HVAC systems

A rating of aircraft "noisiness" used in assessment of aircraft flyover disturbance

Night avei-age sound level (NL) Community noise equivalent level (CNEL) Day/night average sound level (DNL)

Used for assessing annoyance by noise to a community, including various types of day v. nighttime sensitivity weightings

Bels (equal to 10 dB) Used to rate the noise of some ventilation fans

P s y c h o a c o u s t i c s a n d H e a r i n g 43

Figure 3.5 No i s e C r i t e r i a ( N C )

curves. These are used to describe

the target c r i t e r i a f o r the level o f

b a c k g r o u n d noise i n a r o o m . L i k e

the equal-loudness curves s h o w n i n

Figure 3.3, the N C curves c o m p e n -

sate f o r the fact that h u m a n hea r ing

is less sensitive to l o w e r frequencies

than to h ighe r frequencies. I n mea -

surement applications (see C h a p -

ter 4 ) , a par t icular curve is ind ica ted

o n the basis o f the loudest frequen-

cy r e g i o n o f the b a c k g r o u n d noise.

31.5 63 125 250 500 ll< 2I< 4i< 8I<

Octave-band center frequency (Hz)

band sound pressure level i n rooms. These methods f o r ra t ing noise are

per iodica l ly revised or m o d i f i e d as researchers develop n e w insights i n t o

the effects o f noise and v i b r a t i o n o n h u m a n physiology and percept ion.

C o n c l u s i o n

I n this chapter, i t was p o i n t e d out that physical measurements o f sound

f o r m the basis o f psychoacoustic descriptors. Psychoacoustics is a j o i n t

f i e l d o f physics and psychology that deals w i t h acoustical phenomena as

related to aud i t ion . T h e relationship be tween physical acoustic variables

and h u m a n response is n o t l inear and cannot be precisely predicted. A

w i d e var ie ty o f psychoacoustic measures are used to correlate the physical

measurement o f a sound w i t h people's subjective response, depending o n

the specific appl icat ion.

R o o m A c o u s t i c s 93

pet that is f u r r e d over sound-absorbing fibrous board (Figure 6.22) is also

used. This type o f carpet is c o m m o n l y applied to the rear and side waUs o f

movie cinemas. Q u i l t e d sound-absorbing material is also very abuse-resis-

tant (Figure 6.23). I t is available w i t h a massive septum to help reduce sound

transmission. This material is used i n a w i d e range o f situations. For exam-

ple, bafiles are fi-equently h u n g around noisy machinery and larger arrays o f

baffles are suspended o n the waUs o f sound stages and recording studios.

TypicaUy, a substance that prevents air flow in to the porous material

w i U result i n its decreased sound absorpt ion. For example, apply ing b r i d g -

i n g paint or fabr ic backed w i t h a non-porous ( impervious) material

reduces sound absorption. Frequently, acoustical plasters, w h e n repainted,

lose their sound-absorbing properties. I n any case, acoustic plasters and

other spray-applied sound-absorbing treatments rely o n proper applicat ion

i n mul t ip l e coats i n order to create porous cavities (Figure 6.24). W h e n

these treatments are imprope r ly applied, their absorptive properties are

greatly reduced.

Labora tory test reports p r o v i d i n g sound-absorpt ion coefficients are

based on measuring the sound-absorbing materials i n a diffuse field w i t h

A c o u s t i c s

sound s t r ik ing the mater ia l be ing tested at aU angles o f incidence ( random

incidence). Th i s is rarely the case i n actual f i e ld condit ions, since no rma l ly

there is a p r i m a r y d i rec t ion f o r sound s t r ik ing a surface radiat ing f r o m a

stationary source.Where sound incidence is perpendicular to the material ,

a sound-absorpt ion coeff ic ient less than that repor ted may o f t en be

observed. T h e sound-absorpt ion coeff ic ient at perpendicular incidence is

best measured using an impedance tube. Sound-absorbing materials can be

def icient i n absorbing power at perpendicular incidence i n a n a r r o w f r e -

quency range, result ing i n a flutter echo.

Occasionally, laboratories report sound-absorption coefficients exceed-

i n g 1.00. This anomaly is created by edge defraction and the fact that o i f ly

the hor izonta l suiface area o f the material is considered, and the increase o f

surface area (due to the edges associated w i t h the thickness) is ignored.

P a n e l A b s o r b e r s

Typica l ly panel absorbers are n o n - r i g i d , non-porous materials w h i c h are

placed over an airspace that vibrates i n a flexural mode i n response to

sound pressure exerted by adjacent air molecules. C o m m o n panel ( m e m -

brane) absorbers inc lude t h i n w o o d panel ing over f r aming , l i gh twe igh t

imperv ious ceilings and floors, glazing, and other large surfaces capable o f

R o o m A c o u s t i c s

resonating i n response to sound. Panel absorbers are usually most ef f ic ient

at absorbing l o w frequencies. This fact has been learned repeatedly on

orchestra pla t forms where t h i n w o o d panel ing absorbs most o f the bass

sound, robb ing the r o o m o f a quali ty described as " w a r m t h . " TypicaUy, the

m a x i m u m sound-absorpt ion coeff ic ient that can be p rov ided by panel

absorbers is 0.5 i n a relatively nar row-f requency range. M e m b r a n e panel

absorbers can be tuned to a particular frequency. I t is possible to broaden

the f requency range be ing absorbed by adding porous mater ia l i n the air-

space b e h i n d the panel absorber, also caUed cavity damping. T h e resonant

fi-equency o f a panel absorber is typicaUy the f requency at w h i c h m a x i -

m u m absorpt ion w i U occur. T h e resonant f requency can be calculated

using the equation below.

S [md]'/2 [ m d ] ' 2 3

W h e r e f is the resonant f requency (Hz) ; m is the sui-face density, k g / m ^

(psf); d is the depth o f t h e airspace b e h i n d the panel absorber, c m ( in . ) .

Typically, the resonant f requency o f panel absorbers lies be low ^00 H z . T h e

greater the airspace beh ind the membrane and the higher its surface den-

sity, the lower the resonant f requency w U l be. M e m b r a n e absorbers can be

useful f o r he lp ing damp standing waves between 100 and 200 H z . A t y p i -

cal membrane absorber is 6 m m (V4 in . ) tempered hardboard over a 37 m m

(1 V2 m.) airspace conta in ing 25 m m (1 in.) th ick glass fiber.

I t is possible to combine the attributes o f a porous absorber w i t h

those o f a membrane absorber. For instance, a porous absorptive layer cou ld

be surface-applied over a membrane absorber. Specialized porous absorbers

have been developed f o r use i n locations where cleaning is necessary such

as in kitchens and operat ing rooms. I n these cases a t h i n plastic film is

applied over the glass fiber. UsuaUy, the low-f i 'equency absorpt ion is

enhanced by the membranous characteristics o f the film. However , w h e n

the t w o absorbers are combined , the h igh-f requency absorpt ion is some-

wha t compromised.

R e s o n a t o r s

Resonators typical ly act to absorb sound i n a nar row-f requency range; they

include some perforated materials and materials that have openings (holes

and slots). T h e classic example o f a resonator is the H e l m h o l t z resonator,

w h i c h has the shape o f a bot t le . T h e resonant f requency (f^) is governed by

R o o m A c o u s t i c s 97

the size o f the opening, the l eng th o f the neck, and the v o l u m e o f air

trapped i n the chamber.

z o

I A

V ( l + n d )

W h e r e c is the speed o f sound; A is the neck cross-sectional area; / is the

length o f neck; d is the diameter o f the neck opening; n typicaUy varies

be tween 0.85 f o r a smaU neck diameter and 0.60 f o r a resonator w i t h o u t

a n e c k ; V is the chamber vo lume .

Slot ted concrete masonry units ( C M U ) are b u i l d i n g materials that are

based o n the use o f resonators. Slots open the h o l l o w core (or chamber) to

the r o o m (Figure 6.25). O f t e n , these resonators are tuned to relatively l o w

frequencies. For such a resonator to be an efEcient absorber, i t is necessaiy

Figure 6.25 Acous t ica l masonry

units .

98 A c o u s t i c s

to locate the m o u t h o f t h e open ing near an area o f high-acoustic velocity.

UsuaUy, such resonators have fa i r ly nar row tunings and are ideal f o r damp-

i n g standing waves or absorbing sound emi t ted by a tonal source, such as a

transformer.

TypicaUy, perforated materials on ly absorb the mid - f r equency range

unless special care is taken i n designing the fac ing to be as acousticaUy

transparent as possible. (See the discussion o f transparent surfaces earlier i n

this chapter.) Slats usuaUy have a similar acoustic response. T h e amount o f

h igh- f requency absorpt ion is de termined by the d imens ion o f the slat and

its abUity to reflect a particular wavelength, and the space be tween slats

exposing a higher percentage o f absorptive material (Figure 6.26). N o r -

maUy, w o o d griUes w i t h very nar row slats come closest to having the same

absorption characteristic as the sound-absorbing material be ing covered.

L o n g , na r row slots can be used to absorb l o w frequencies. For this

reason, l ong , na r row air d i s t r ibu t ion slots i n rooms f o r music p r o d u c t i o n

should be v i ewed w i t h suspicion since the slots may absorb valuable l o w -

firequency energy. For example, i n a music recording stage specificaUy

R o o m A c o u s t i c s 9 9

designed to have variable reverberation times by using s l iding sound ab-

sorptive panels, an interesting sound-absorbing p h e n o m e n o n occurred

(Figure 6.27). W h e n the sound-absorbing panels were pu l l ed ou t o f t h e

slots and exposed i n the r o o m , the reverberation t ime was reduced, except

at frequencies b e l o w 80 H z . W h e n the absorptive panels were i n the slots,

the r o o m reverberation increased except at frequencies b e l o w 80 H z . W h y

d i d the l o w frequencies behave differently? A 19 m m ( 4 in . ) gap, 10 m

(31 f t . ) l ong , was created w h e n the panels were i n the slots. T h e slots were

filled w i t h the concealed 100 m m (4 in.) t h i c k sound-absorbing material .

NormaUy, w i t h sound-absorbing material concealed i n the slots, a longer

reverberation t ime is expected. Th i s reversal can be a t t r ibuted to the

absorpt ion si t t ing i n the unsealed slots, w h i c h absorb more sound be low

80 H z than w h e n the absorptive panels are ou t o f t h e slots and exposed i n

the r o o m . T o el iminate the l o w - f r e q u e n c y paradox, the slots must be sealed

w h e n the sound-absorbing mater ia l is concealed i n the slot.

1 00 A c o u s t i c s

A i r A b s o r p t i o n

Sound absorpdon i n air can be significant i n rooms larger than 2,800 m ^

(100,000 c u . f t . ) i n a f requency range above 1 k H z . A i r absorption becomes

m u c h more significant at relative humidi t ies be low 30 percent. I n music

halls hav ing large i n t e r i o r volumes, air absorpt ion is o f t en responsible f o r

the reduced reverberation t ime at h i g h frequencies w h e n compared to the

mid-fi"equency range. A i r absorpt ion i n a r o o m is directly p ropor t iona l to

the distance traveled by the reflected sound p r i o r to reaching the listener;

absorpt ion is therefore greater in larger rooms.

I V . M u s i c H a l l E v a l u a t i o n a n d A c t i v e A c o u s t i c s

T H E final assessment o f t h e suitabil i ty o f a room's acoustics is subjective and

entirely dependent u p o n h u m a n perceptions and preferences. W h i l e

acousticians have had the abi l i ty to measure sound pressure level and rever-

bera t ion t ime f o r decades, the subjective impression o f reverberance has

no t always correlated w e l l w i t h the objective measurement. I n addi t ion , the

t e r m i n o l o g y describing the subjective impressions has been p o o r l y stan-

dardized u n t i l recently. I n order to have a mean ing fu l discussion, i t is nec-

essary to standardize the te rminology, as indicated i n Table 6. 2.

Table 6.2 Standard t e r m i n o l o g y . Subjective term Description of precept Proposed objective measure

Loudness Strength or loudness of a sound Total sound (pressure) level

(Source strength)

G (A-weighted)

Clarity Articulationthe ability to hear Early-to-late sound r a t i oC ^ q ,

definition and detail, often relating Cgo (level adjusted)

to speech or faster tempo music

Intimacy Apparent closeness of sound I T G or "Initial time gap"

Reverberance Perception of reflected sound Early sound reflections, E D T

and liveness (125 Hz to 4 kHz S E G ratio,

ISE-T5)

Envelopment Immersion in a sound field, the sense Late lateral sound level (after

of being surrounded 80 msec)

Brightness Relative loudness of treble or high 2 to 4 kHz sound level and

frequency sounds compared to reverberation time

mid-frequency sound

Bass warmth The relative loudness of bass or low Early low frequency sound

frequency sounds compared to the level125 to 500 Hz values

mid-frequency sounds of G in the first 50 msec

T h e next section contains def ini t ions f o r the object ively measurable

parameters that are then related to subjective impressions i n the section

that foUows. FoUowing these t w o sections, the field o f active acoustics is

b r i e f l y discussed.

R o o m A c o u s t i c s 101

O b j e c t i v e P a r a m e t e r s

Reverberation time (T) is the t ime i t takes the reflected sound to decay

60 dB subsequent to the abrupt cessation o f the sound source.

Source strength (G) is the ratio o f sound pressure level compared to

the reference level o f the direct sound field w i t h o u t reflections measured

at 10 m (33 f t . ) f r o m the same source. I n concert hahs, the values typ ica l -

ly range be tween 0 and + 1 0 dB, demonstrat ing the ampl i f i ca t ion p rov ided

by r o o m reflections.

The early-to-late sound ratio (Cla r i ty (C40, Cgg)) is the sound pressure

level i n c l u d i n g the direct- and early-reflected sound (up to 40 msec f o r

speech and up to 80 msec f o r music), d iv ided by the total sound energy

a r r i v ing after 40 and 80 msec respectively. C^ can be estimated f r o m the

f o l l o w i n g equation:

z c C , = 10 l o g

10

T T (0.04i-+13.82t)/T ^ g(13.82t/T) _ ^

312Tr2

Where C^ is clarity; t is the t ime (sec), def in ing the extent o f t h e early sound

field (usuaUy 0.04 or 0.08); r is the distance fi-om the sound source m ( f t . ) ;T

is the reverberation t ime. (See Append ix 1 fo r predicted values o f C j fo r a

12,000 m3 (39, 372 cu. f t . ) haU at vary ing distances and reverberation times.)

C40 values o f + 5 dB are considered good f o r speech inteUigibi l i ty ,

w h i l e those less than 0 dB are poor . Cgg values considered desirable are

+ 5 dB f o r electronicaUy ampl i f i ed music, 0 dB f o r classical music, and -2

dB f o r romant ic classical music.

Lateral energy fraction compares the sound energy a r r i v i n g lateraUy

w i t h the sound energy a r r i v ing f r o m aU directions. I t has been shown that

this measurement does not account f o r aU spatial effects heard by listeners,

and that no parameter yet measures the subjective diffuseness o f a rever-

berant sound.^ T h e acceptable range o f var iat ion i n early (0-80 msec) lat-

eral energy f r ac t ion is 0.1 to 0.35 f o r unoccup ied music haUs w i t h the la rg-

er value be ing preferred.

Interaural cross-correlation ( l A C C ) is the degree o f corre la t ion be tween

signals a r r i v ing at a listener's ears. l A C C rates on a scale o f 0 to 1.

Early decay time ( E D T ) is the in i t i a l reflected sound decay def ined as

"the slope o f t h e early sound decay o c c u r r i n g i n the first 10 dB o f decay

normal ized to 60 dB, m a k i n g i t comparable to reverberation t ime." I n a

perfect ly diffuse sound field, the early-decay t ime w o u l d be equal to the

reverberation t ime. This is the case i n many concert halls. However , i n

some haUs, where reverberance is less apparent, the early-decay t ime is less

than the reverberation t ime due to a lack o f early-reflected sound.

Sound energy growth (SEG) curve is a new parameter depict ing the

g r o w t h i n sound energy d u r i n g the first 200 to 300 msec (Early and M i d d l e ) .

Instantaneous sound envelope (ISE) is a n e w parameter y i e ld ing the

A c o u s t i c s

sound ampli tude and arrival t ime o f ind iv idua l reflections. ISE is especial-

ly useful f o r comparison w i t h calculated reflectograms generated i n c o m -

puter models. ISE shows ind iv idua l reflections c o n t r i b u t i o n to the SEG

(See Figure 6.36 i n A p p e n d i x 3) . T h e author's i n t en t i on i n i n t r o d u c i n g

these t w o n e w terms is to provide a better comparison between measure-

ments (ISE), calculations ( f r o m ray or image computer models), and sub-

ject ive impressions (SEG) based o n energy parameters.

Initial time gap ( I T G ) is the t ime between the direct sound arrival at

a Hstener and the first reflections. For good concert acoustics, the I T G

should no t exceed 20 msec.

S u b j e c t i v e i m p r e s s i o n s

I t is weU k n o w n that the subjective impression o f reverberance is no t sole-

l y a f u n c t i o n o f the reverberation t ime, bu t rather a relationship between

sound-energy g r o w t h , early-decay t ime, eai iy-to-late sound ratio, and the

specific type o f p rog ram material be ing transmitted. Reverberance is m u c h

more apparent w h e n l is tening to speech than to classical music, due to the

need f o r greater ar t icula t ion. Simflarly, fast tempo percussive music, such as

jazz, is more easily " m u d d i e d " by reverberation than is classical music.

Classical music o f the romant ic p e r i o d can tolerate stiU longer reverbera-

t i o n times. Baroque organ music can thr ive o n l o n g reverberation times o f

3 to 6 seconds. I t is possible f o r a hstener to perceive the same level o f

reverberance i n very d i f ferent spaces. For instance, similar impressions o f

reverberance can be had m a 5,700 m-^ (200,000 cu. ft.) r o o m having a

reverberation time o f 2 seconds as i n a 57 m ^ (2,000 cu. f t . ) space w i t h a

reverberation t ime o f 0.5 seconds!

O n e interesting study, w h i c h is based o n subjective impressions, i n d i -

cates that concert hsteners may fa f l i n t o t w o preference groups: those w h o

prefer reverberance and those w h o prefer int imacy. This same study also

revealed parameters strongly correlated to overaU acoustic impression as

indicated graphicaUy i n Figure 6.28.

T h e l i n k be tween the subjective impression parameters and the

objective measurement parameters is current ly an area o f intense study.

Recently, the vahd frequency ranges f o r certain parameters were iden t i f i ed

as foUows: (1) early-decay t ime: 125 f i z to 4 k H z ; (2) early-to-late sound

ratio: 500 H z to 2 k H z ; (3) sound strength: 125 H z to 4 k H z ; (4) lateral

energy f rac t ion : 125 H z to 1 k H z .

O t h e r research results indicate h i g h levels o f corre la t ion be tween

loudness and A - w e i g h t e d source strength. Reverberance was f o u n d to be

h igh ly correlated w i t h early-decay t ime. C la r i t y was f o u n d to h igh ly cor-

relate w i t h the early-to-late sound ratio averaged over the 500 H z and 1

k H z bands. Brightness (treble) was f o u n d to h igh ly correlate w i t h late

sound strength (after 80 msec) subtracting the 1 and 2 k H z average value

fiom the 4 k H z value.

R o o m A c o u s t i c s

Figure 6.28 Re l a t i onsh ip o f acoust i -

cal terms based o n subjective

impressions.

A c t i v e A c o u s t i c s

Act ive acoustics is the emerging field o f enhancing natural acoustics w i t h

an electroacoustic system employ ing a digi ta l reverberation processor.

W h i l e the concept o f adding electronicaUy generated reflections to those

prov ided by the r o o m is no t new, recently, the abi l i ty to synthesize elec-

tronic reflections, w h i c h cannot be distinguished f r o m those o c c u r r i n g

naturaUy, has become easier. This field has a b r i g h t fu tu re ; its applications

include b o t h n e w cons t ruc t ion and re t rof i t i n exist ing bui ld ings .This f o r m

o f active acoustics adds the electrorucaUy generated sound field to that p r o -

v ided by the r o o m , u i f l i ke active noise cont ro l , w h i c h seeks to reduce the

sound level t h rough sound field canceUation. Ac t ive acoustics potentiaUy

aUows f o r the design o f mult iuse facUities based o n speech. For music, the

space can be made more reverberant w i t h more early reflections b y using

an active sound field. Ac t ive acoustics can potent ia l ly be imp lemen ted

using as f e w as t w o appropriately placed microphones and a d ig i ta l rever-

berat ion processor having t w o inputs and f o u r outputs. Recent ly, such sys-

tems have been imp lemen ted successfuUy i n the E l g i n Theater i n Toronto ,

the Lu the r Bu rbank C o m m u n i t y Arts Center i n Santa Rosa, and the Tsai 12

Center at Bos ton Universi ty.

U n t f l now, the implementa t ion o f such systems has been slow due to

the lack o f enthusiasm f o r electronics and electroacoustics i n the apphcation

where their benefits w o u l d be most feltclassical music. This , however, is

changing, i n large part due to the active role electronics are playing i n our

dafly lives. I f electronicaUy enhanced reverberance cannot be distinguished

f r o m natural reverberance produced i n the best haUs, then w i d e acceptance

f o r electronicaUy assisted reverberance should foUow. O n e m a j o r advantage

o f synthesized reverberation is that i t can be adjusted to suit a particular per-

formance or performance-venue conf igura t ion , part icularly those where

seating plans are variable. F r o m the architectural standpoint, provisions need

to be made f o r an array o f loudspeakers concealed w i t h i n the waUs and cef l -

1 04 A c o u s t i c s

i n g o f a reverberance-enhanced space. Concealing loudspeakers remains a

challenge where smooth wal l and ceil ing suifaces occur.

C o n c l u s i o n

Is r o o m acoustics an art or a science? This chapter has explored that ques-

t i o n by iUustrating the connec t ion between newer sound-measurement

techniques and aural impressions f o r m e d by listeners' preferences. Recen t

technology has ref ined the acoustician's abihty to predict a room's acousti-

cal requirements. I t is n o w possible, fo r example, to provide active acousti-

cal enhancement by i n t roduc ing synthesized sound reflections t h rough an

array o f loudspeakers, thus i m p r o v i n g the quali ty o f the transmitted sound

dramaticaUy. M o r e specific design cr i ter ia are also evolv ing to suit different

uses. A c k n o w l e d g i n g the uniqueness o f t h e design cr i ter ia required f o r each

space is v i ta l to the success o f the facil i ty, especiahy i f i t is mul t ipurpose .

A r t imphes i n t u i t i o n and mastery. Science can aid i n the develop-

men t o f b o t h . B u t w h a t role does l u c k play? Were the grand masters s im-

ply lucky? Is i t l uck or skiU that aUows an artist to appeal to a broad audi -

ence? I t is i n fact a c o m b i n a t i o n o f bo th . Today's r o o m acoustics, l ike many

arts, is an o p i n i o n - d o n f i n a t e d field, one that is i n f luenced as m u c h by his-

t o r y as i t is by technology.

R o o m A c o u s t i c s 105

References

1. F l o y d T o o l , "Speakers and R o o m s

f o r S tereophonic S o u n d

R e p r o d u c t i o n . " (proceeding o f

A u d i o E n g i n e e r i n g Society E i g h t h

In t e rna t i ona l Conference , 1990)

2. Joseph M i l n e r and R o b e r t

Be rnha rd , " A n Invest igat ion o f the

M o d a l Characterist ics o f

N o i i r e c t a n g u l a r R e v e r b e r a t i o n

Rooms."_//Yr/7/ of the Acoustical

Society of America, v o l . 85, no. 2

(February 1989).

3. T J . Shultz, " R o o m Acoust ics i n

the Des ign and Use o f Large

C o n t e m p o r a r y C o n c e r t Halls ." ( p r o -

ceedings o f t h e 12 th In te rna t iona l

Congress on Acoust ics , 1986).

4. Y.Toyota and M . Nagata et a l . , " A

Study o f R o o m Shape o f C o n c e r t

H a l l s " ( technical paper G A A pre -

sented at 120th Acous t i ca l Society

o f A m e r i c a , N o v e m b e r 1996).

5. L e o L . Beranek, Concert and Opera

HaUs: How They Sound (Acoust ical

Society o f A m e r i c a , 1996).

6. M . B a r o n and L . Lee, "Energy

Rela t ions i n C o n c e r t A u d i t o r i u m s . "

Journal of the Acoustical Society of

America, v o l . 84, no. 2 (August 1988)

pp. 6 1 8 - 6 2 8 .

7. T J . Shultz, "Acous t i ca l Uses f o r

Perforated Mater ia ls : Pr inciples and

A p p l i c a t i o n s " ( Indus tna l Perforators

Associat ion, 1986)

8 M . Baron and L . Lee, pp. 6 1 8 - 6 2 8 .

9 D . S c h w i n d and A . Nash, et a l ,

" T h e Early S o u n d F ie ld i n Pe r fo r -

mance H a l l s " ( A u d i o E n g i n e e r i n g

Society P rep r in t 4108 . 99 th C o n -

v e n t i o n , O c t o b e r 1995).

10. D . Griesinger, "Subjec t ive

Loudness o f R u n n i n g R e v e r b e r -

a t i on i n Hal ls and Stages" (proceed-

ings o f W C . Sabme C e n t e n n i a l

Sympos ium, June 1994) , pp . 8 9 - 9 2 .

1 1 . G. Soulodve and J. B r a d l e y

"Subject ive Eva lua t ion o f N e w

R o o m Acous t ic Measures." Jowrna/ of

Acoustical Society of America, v o l . 98,

no. 1 (July 1995) pp. 2 9 4 - 3 0 1 .

12. D . Griesinger, pp. 89 -92 .

106 A c o u s t i c s

V . A p p e n d i c e s

This section is f o r the reader w h o seeks more technical i n f o r m a t i o n about

detailed calculations and measurements o f r o o m acoustics. T h e techniques

ou t l ined i n this appendix demonstrate that the gap is closing between

acoustical calculadons and results measured i n real spaces. For example, the

reader is i nv i t ed to compare the calculated data o f A p p e n d i x 1 w i t h the

measured results presented i n A p p e n d i x 3. A l t h o u g h i t should be kept i n

m i n d that the hall dimensions vary, and, as indicated i n Table 6.5, trends i n

the data are readily apparent.

A p p e n d i x 1: E a r l y S o u n d F i e l d C a l c u l a t i o n s

C o m p a r i s o n o f T h r e e M u s i c P e r f o r m a n c e H a l l S h a p e s

Three different concert hall shapes are compared using a computer program

based o n a ray-tracing a lgo r i t hm called " O d e o n " Version 2.6D. T h e three

hall shapes compared are the shoebox, the fan, and the reverse fan . N o n e o f

the halls have balconies. T h e sound source (sl) has been placed i n compa-

rable positions and receivers (listeners) are located 10, 20, and 30 meters

f r o m the stage l ip . T h e 30-meter pos i t ion only apphes to the reverse-fan

shape, due to its greater l eng th .The haU volumes are ah 12,000 cubic meters

corresponding to audience capacities o f approximately 1,200. T h e stage

sizes are aU similar, corresponding to 200 square meters. Three dimensional

views o f t h e halls, shown as w i r e f rame models, are depicted i n Figures 6.29,

a, b, and c, and show receiver positions near the center and sides.

Figure 6.29 C o n c e r t H a l l W i r e

f rame models: (a) shoebox;

(b) w i d e fan ; (c) reverse fan .

Figures 6.30 a, b, and c ah depict the halls w i t h the source (sl) o n the lef t

and receiver (r2) o n the r igh t , located 20 meters f r o m the stage l ip . Paths

o f sound propagat ion shown as rays emanating f r o m the source are on ly

depicted f o r those reaching the receiver. O n l y first and second-order

reflections are shown. Figures 6.30 a, b, and c also depict polar plots o f i n c i -

dent sound at the receiver i n the hor izonta l -p lan v i e w and polar plots o f

the inc ident sound i n the vertical view. I n b o t h cases, the listener is fac ing

the stage o n the le f t side o f the page. These polar plots correspond to the

three haU shapes and the relative source-receiver positions indicated. Polar

plots show the d i rec t ion and intensi ty o f sound received by the hstener. I n

R o o m A c o u s t i c s

compar ing the hor izon ta l polar responses, note that the inc iden t sound

from the front d i rec t ion is narrower fox the f an and w i d e r f o r the reverse

fan than f o r the shoebox. These data indicate the reverse f a n should create

a greater sense o f spaciousness and envelopment.

Figures 6.31 a, b, and c are cross-sectional end views w h i c h face the

stage and show b o t h source and receiver (r4) locations. N o t e that the

receivers are at a higher elevation, due to the f l o o r slope. Figure 6.31a f o r

Figures 6.30 a, b, and c {top to

hottoin) (a) shoebox ref lect ions; (b)

f an ref lect ions; (c) reverse f an ref lec-

t ions. Re f l ec t ions received by the

hstener are ind ica ted i n the h o r i -

zonta l and ver t ica l planes.

1 08 A c o u s t i c s

the shoebox clearly shows the receiver obta in ing reflections from b o t h

sidewalls v ia the cei l ing. Figure 6.31c indicates numerous such reflections.

T h e fan shape i n Figure 6.31b shows the sound-ref lect ing canopy over the

stage a id ing the recept ion o f on ly one re f lec t ion fr'om the house r i g h t waU.

N o t e the relative w i d t h o f the three proposed hall shapes, the f an be ing

widest and the shoebox narrowest.

Figures 6.32 a, b, and c correspond to the three hah shapes and iUus-

trate the tempora l d i s t r ibu t ion o f early reflections and their relative a m p l i -

tude along w i t h the i n i t i a l t ime delay gap. Ref lec t ions up to the t h i r d order

are shown.

Figure 6.31 a, b, e C o m p a r i s o n o f j h e shoe box has an I T G (In i t ia l T i m e Gap) o f approximately sidewall and ce i l i ng ref lect ions:

20 milliseconds, whereas the other t w o shapes have I T G s of approximate-(a) shoebox; (b) f a n ; (c) reverse f a n .

l y 40 miUiseconds f o r a listener at r2 , w h o is located approximately

20 meters f r o m the stage.The I T G o f t h e f an and reverse fan-shaped haUs

cou ld be reduced by l o w e r i n g or stepping the cef l ing d o w n at the stage

end o f t h e haU.This m o d i f i c a t i o n , however, cou ld have an adverse impact

o n r o o m v o l u m e and overaU reverberation t ime. A n alternative to l o w e r -

i n g the cei l ing, is to suspend large sound-ref lect ing panels, w h i c h w o u l d

no t affect r o o m vo lume .

N o t e the relative density and number o f early reflections shown o n

the le f t side o f Figures 6.32 a, b, and c. T h e reverse fan o f Figure 6.32c is

superior i n this regard.

T h e r i g h t sides o f Figures 6.32 a, b, and c show estimates o f the

reverberant decay. T h e upper hne is smooth and represents the reverse-

integrated decay and the lower l ine is typical o f a single decay due to an

impulse w i t h o u t averaging. Large positive peaks w e l l above the adjacent

data are indicative o f potent ia l echoes. This is o f particular concern f o r the

fan-shaped haU. Also note the longer p e r i o d the sound level is sustained

equivalent to the direct sound f o r the reverse fan; the decay does not beg in

immediately, bu t instead aUows the reverberance to " b l o o m . " T h i s accounts

f o r a longer early-decay t ime , w h i c h corresponds to haU "liveness."

Table 6.3 compares the three haU shapes by listener loca t ion . N o t e

that the number o f early reflections increases near the waUs and toward the

rear o f the halls i n all cases. Also note that i n aU cases, the reverse f a n has a

higher total number o f reflections foUowed by the shoebox and the fan .

N o t e that the early decay times at 500 H z f o r aU listener locations i n the

reverse f a n haU are typical ly longer than the other shapes. Table 6.3 also

R o o m A c o u s t i c s 1 09

80

70

60

50

40

30

20

0 -50 0 50 100

Seconds (re. direct sound) Reverberation decay

80

compares the L E F (Lateral Energy Fract ion) , w h i c h is most consistent i n

the shoebox but rises to h igher levels i n the reverse fan.

Figure 6.33 compares the listener locations 10 and 30 meters ( r l and

r5) f r o m the stage. N o t e the higher density o f early reflections i n the more

distant seat. This t rend can also be seen w h e n compar ing receiver loca t ion

r2 to r5 i n Table 6.3.

Figure 6.32 a,b, and c Calculateid

early (left) and late {right) s o u n d

reflect ions f o r the situations dep ic t -

ed i n Figure 6 . 3 1 : (a) shoebox; (b)

fan ; (c) reverse fan .

1 10 A c o u s t i c s

Narrow Fan Listener locations Shoe Box Listener locations Reverse Fan Listener locations

Reflection Orders Rl R2 R3 R4 Reflection Orders Rl R2 R3 R4 Reflection Orders Rl R2 R3 R4 R5 R6

1st 7 7 7 7 1st 5 7 5 7 1st 8 8 8 8 8 8

2nd 12 19 14 19 2nd 13 19 15 20 2nd 21 22 20 24 29 29

3rd 16 28 24 28 3rd 27 33 29 25 3i-d 24 36 28 33 46 49

Total Reflections 35 54 45 54 Total Reflections 45 59 49 63 Total Reflections 51 66 56 65 83 86

LEF @ 500Hz 0,03 0.11 0.26 0.16 LEF @ 500 Hz 0.16 0.17 0.27 0.19 LEF @ 500Hz 0.06 0.26 0,18 0.34 0.28 0.31

E D T (T=l.7) 1.7 1.8 1.6 1.7 E D T (T= 1.8) 1.9 1.8 1.8 1.9 E D T (T=l.7) 1.9 2.4 2.2 2.3 1.9 2.0

Table 6.3 C o m p a r i s o n o f hal l

shapes at various listener locat ions .

T h e n u m b e r o f reflect ions are hsted

b y r e f l ec t ion order. Calcula ted

Latera l -Energy f ract ions (LEF) and

Ear ly -Decay T i m e s ( E D T ) are l i s ted

by listener l oca t ion .

Figure 6.33 Reverse f a n data f r o m

listener locations 10 and 30 meters

f r o m the stage.

70

m 60

> 50

5 40

-30

: 20

10

70

~ 6 0

3 SO

3 40

30

20

10

Horizontal

10 20 30 40

Seconds (re. direct sound)

50 Vertical

Horizontal

-50 0 SO 100 150

Seconds (re. direct sound)

200 Vertical

E a r l y - t o - L a t e S o u n d I n d e x C a l c u l a t i o n s

T h e results o f early-to-late sound index (clarity) calculations using

Equat ion 6.11 are presented f o r 40 mil l isecond (Figure 6.34) and 80 nail-

lisecond (Figure 6.35) integrat ion times i n the halls having a vo lume o f

12,000 cubic rneters.The 40 milliseconds in tegrat ion t ime is norrnaUy used

to assess speech and 80 milliseconds is used f o r classical music .The results are

displayed i n a three dimension p lo t as a f u n c t i o n o f listener distance from

the sound source and the haU's reverberation t ime. I n b o t h cases, note the

higher levels o f clarity at reduced reverberation times and near the source.

R o o m A c o u s t i c s 1 1 1

Figure 6.35 Ea r ly - to - l a t e sound

index CgQ for a ha l l v o l u m e o f

12,000 m 2 .

^""^sto . " " 23

10.00- i2,00 8 .00 - 10.00 6 .00 - 8,00 4 . 0 0 - 6.00 2 . 0 0 - 4.00 0 .00 - 2.00 -2.00 - 0,00 -4.00 - -2.00

A p p e n d i x 2 : R e v e r b e r a t i o n T i m e C a l c u l a t i o n U s i n g S a b i n e ' s E q u a t i o n s

Table 6.4 is an example o f a typical reverberation t ime calculation most

c o m m o n l y used by acoustical engineers f o r the last n ine ty years. A b s o r p -

t i o n coefficients are m u l t i p l i e d by the surface area to obtain a total number

o f sabins f o r each surface and material . T h e total absorption is summed i n

each octave band fo r use w i t h Sabine's equation (Equat ion 6.2). These

reverberation times are based o n statistical probabi l i ty and may di f fer f r o m

the results obtained using ray-tracing algorithms. This difference is more

evident f o r the case o f unevenly dis t r ibuted sound-absorbing material i n

spaces having large aspect ratios such as very l o n g and na r row spaces. I n this

example, a reverberation t ime o f 2.2 seconds at 500 H z agrees reasonably

w i t h the ray-tracing results.

1 1 2 A c o u s t i c s

Absorption Coefficients

Material Surface 125 250 500 1,000 2,000 4,000

60 mm plaster Ceiling 0.10 0.05 0.04 0.03 0.03 0.03

2 layers of gypsum board Walls 0.20 0.14 0.12 0.1 1 0.10 0.09

25 mm sound absorbing panel Rear wall 0.09 0.32 0.76 0.95 0.99 0.99

Wood over space Stage 0.15 0.1 1 0.10 0.07 0.06 0.07

Audience Main floor 0.72 0.79 0.86 0.88 0.88 0.88

Sabins (m^)

Surface Area (m^) 125 250 500 1000 2000 4000

Plaster Ceiling 812 81 41 32 24 24 24

Gypsum board v/alls 1409 282 197 169 155 141 127

Sound absorbing panel rear wall 265 24 85 201 252 262 262

Wood stage 300 45 33 30 21 18 21

Audience 514 370 406 442 453 453 453

Air absorption (sabins) 0 0 0 0 24 96

Totals 3300 802 762 874 905 922 983

Octave band reverberation time (sec.) 2.4 2.5 2.2 2.1 2.1 2.0

Table 6.4 R e v e r b e r a t i o n t i m e ca lcu- A p p e n d i x 3 : E a r l y S o u n d F i e l d M e a s u r e m e n t s

l a t i o n .

I n t r o d u c t i o n

I n a per formance haU, the early sound f i e l d estabhshes its "signature sound"

and is responsible f o r many o f t h e haU's subjective attributes. T h e temporal

d i s t r ibu t ion o f sound a r r i v ing w i t h i n the first quarter second seems to be

largely responsible f o r the perceived "liveness" o f the haU. U s e f u l tech-

niques f o r examin ing the early sound field are the measured sound energy

g r o w t h (SEG) curve and instantaneous sound envelope (ISE).These tech-

niques examine sound g r o w t h rather than decay. I n addi t ion to p r o v i d i n g

a clear, easy-to-interpret data presentation, t radi t ional parameters such as

early-to-late sound index (Cgo), rise t ime , and the in i t i a l - t ime-de lay gap

can be extracted or read direct ly f r o m these curves (Figure 6.36). Th i s

alternative data presentation is in tended to help correlate integrated sound

energy parameters to the overall response o f t h e haU as weU as to subjec-

tive response. T h e re f lec t ion energy cumulat ive curve ( R E C C ) is another

descriptor i n v o l v i n g the g r o w t h o f early sound reflections. T h e R E C C ,

however, does no t inc lude the direct sound. M o s t impor tant ly , the c o n t r i -

b u t i o n o f i nd iv idua l reflections (ISE) to the g r o w t h o f sound energy (SEG)

can readily be seen.

R o o m A c o u s t i c s 1 1 3

M e a s u r e m e n t s

A number o f recorded impulses i n per formance spaces have been col lect-

ed. T h e acoustical exci ta t ion f o r these measurements is generated using

either a baUoon burst or by firing a starter's pistol . B o t h methods provide

suitable test spectra. A ba l loon burst results i n a relatively " p i n k " spectrum

(equal sound energy i n any constant percentage bandwid th ) . T h e pis tol

produces more o f a " w h i t e " spectrum (equal sound energy i n any constant

bandwid th ) . T h e pistol also produces a h igher ou tpu t level, w h i c h improves

the signal-to-noise ratio i n larger spaces. T h e b a n d w i d t h o f these test sig-

nals spans the f o u r octave bands f r o m 250 H z to 2 k H z . Since these sources

have relatively constant sound power f r o m impulse to impulse, i t is possi-

ble to make mean ing fu l in te r - and intra-haU comparisons f o r the purpose

o f evaluating loudness.

These recorded signals were processed w i t h the H i l b e r t Transform to

obtain a magnitude, or "envelope" f u n c t i o n referred to as the instantaneous

sound envelope or ISE (see Figure 6.36). T h e ISE depicts the arrival o f the

direct and reflected sound at the measurement mic rophone subsequent to

a test impulse. T h e advantages o f this presentation are: (1) the magni tude

can be displayed o n a logar i thnnc ampl i tude scale, and (2) the delay

between arrivals is easier to discern than o n a tradi t ional osciUoscope dis-

play. T h e first peak i n the ISE is sound a r r i v ing direct ly f r o m the source.

Later peaks represent r o o m reflections. ISE is simflar i n data presentation

f o r m a t to the energy time curve ( E T C ) ; the difference is that the E T C is

derived f r o m an electric (stimulus-response) measurement, whereas the ISE

is the result o f a measured acoustical impulse.

20

15

S 10

5 h

/ D i r e c t Sound

First Ref lect ions

-25

I n addi t ion to the ISE, the recorded signal was squared and integrat-

ed over t ime. Th i s f u n c t i o n is referred to as sound energy g r o w t h , or SEG,

also shown in Figure 6.36. T h e SEG depicts the b u f l d - u p o f sound energy

d u r i n g the first 200 msec.

W h e n the SEG and ISE are p lo t t ed on the same t ime axis, the c o n -

t r i b u t i o n o f ind iv idua l reflections to the g r o w t h o f sound energy can be

seen. For example, significant time delays between arrivals i n the ISE result

i n plateaus i n the SEG.

200

Figure 6.36 Instantaneous S o u n d

Envelope (ISE) and S o u n d Energy

G r o w t h (SEG). ISE represents the

magni tude o f t h e sound pressure at

the m i c r o p h o n e as a result o f an

acoustical hnpu l s e .The SEG depicts

the b u i l d - u p o f early sound energy.

1 1 4 A c o u s t i c s

D i s c u s s i o n

Figure 6.37 a t h r o u g h d contains comparative data f o r t w o music pei-for-

mance haUs, a scor ing stage, and a f i l m screening r o o m . A h data were ana-

lyzed using the ISE and SEG techniques. These figures ah appear o n the

same relative ampl i tude scale f o r comparison. Several o f these facilities have

received h i g h cr i t ica l acclaim f r o m musicians, audiences, and the media.

Three o f these facilities are discus