AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 10 -

IMPORTANCE OF EARLY ENERGY IN ROOM ACOUSTICS

!

There are three important aspects of the early part of a room's impulse response,

a)

Echo

b)

Colouration

c)

Support

!

An human ear acts as a short time integrator - hence ability to resolve succeeding
acoustic events is restricted (termed the 'inertia' of hearing).

!

Question:

What are the conditions for a reflection or reflection sequence to
appear as a disturbing echo, to change the timbre of the original
signal (colouration), or merely to support the original sound ?

The answer to the question is important so that one can design to avoid the first two
effects and to get the benefit of the last.

Echoes

1950 Haas : Continuous Speech
(figure) [Acustica 1, 1951, p.49]

Subjective testing showed
that the % of test subjects
d i s t u r b e d b y o n e s i n g l e
reflection following the direct
sound signal depends on

1) level of the reflection relative
to direct sound level

2) delay time of the reflection
from the direct sound

A higher level is required to disturb at a shorter delay time, i.e. the earlier the
reflection the less chance it will appear as a disturbing echo.

The figure shows that the % disturbed changes very little when the level is
increased from 0 to 10dB, but increases significant from -10dB to 0dB, which
unfortunately is the range of levels usually found in real halls.

One very significant result from Haas's work is the
Haas' effect

-

no disturbance is expected for delay < 20ms even with

a

reflection

level of +10dB.

Generally curves in the figure shift upwards (more disturbing) with faster speaking
rate and shorter RT of the test room.

In practice the level of the 1st reflection in a real hall lies between -3dB to 0dB.
Within this range the sharp rise of the % disturbed occurs at delay times around 40-
60ms.

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 11 -

1953 Muncey et al : Speech as well as Music (figure) [Acustica 3, 1953, p.168]

Critical echo level -
the reflection level
at which 50% of the
test subjects were
disturbed.

Their work clearly
shows that hearing
is less sensitive to
echo disturbance in
m u s i c t h a n i n
speech - since music
does not have to be
'understood' in the
same sense as in
speech.

Annoyance of echoes is lower for slower music
e.g.

for (a) organ music:

at 80ms delay the critical level is

.

+10dB

for (b) fast string music:

at 80ms delay the critical level is

.

-3dB

1952 Meyer and Schodder : Speech (figure) [Math.-Phys. Kl. 6, 1952, p.31]

T e s t s u s i n g
reflections with a
lateral angle of 90°.
Results similar to
those of Haas but
more detailed and
precise.

Also shows that if a
reflection is split up
into several small
reflections with a
s u c c e s s i v e m u t u a l
delay time of 2.5ms,
leaving constant the
centre delay time and the total reflection energy, then about the same
disturbance will occur (the curves may shift upwards by 2.5dB at most).

The above investigations show that generally echo disturbance occurs only at
exceptional cases. Generally the law of first wave front holds, i.e. the localization and
characteristics of source depends on the first wave arriving at the receiver (direct
sound). Exceptions (e.g. echoes) only occur in special situations where an exceptionally
strong reflection arrives at a late delay time.

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 12 -

(22)

(23)

Colouration

At a short time delay t

o

, a strong reflection

(or successive, regular reflections with
mutual delay time t

o

) may not be perceived

as an echo but causes the undesirable effect
of colouration - a characteristic change of
timbre.

The threshold of colouration is shown in
the accompanying figure as a function of
delay time. The threshold is lowest (most
disturbing) below 20ms but rises sharply
(less of a problem) with delay time above
20ms [Atal, Schroeder & Kuttruff, Proc. of
the 4th ICA, 1962, H31].

When the successive mutual delay time is
greater than a certain limit (say 25ms), the
perception of colouration turns into a
perception of rough characters (flutter
echoes - perception of regular repetition of
the signal).

Detection of echoes and colouration

Echoes and colouration may be detected by visual examination of the room's impulse
response with the aid of the preceding knowledge, or by

Echo Criterion [Dietsch L. & Kraak W. Acustica 60, 1986, p.205]

Based on the temporal build up of the impulse response. Defines

The echo criterion EC is then

Values of n and

)J

depend on the source. The following is suggested

(EC

critical

the value that should not be exceeded to ensure no more than 50%

of the listener will hear an echo).

n

)J

(ms)

EC

critical

Bandwidth (Hz)

Speech

2/3

9

1.0

700-1400

Music

1

14

1.8

700-2800

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 13 -

(24)

(25)

Colouration

[Kuttruff H. 'Room Acoustics' 3rd Ed., 1991, p.235]
[Bilsen F.A. Acustica 19, 1967/68, p.27]

Based on autocorrelation analysis. Let

N

gg

(

J

) be the autocorrelation function of the impulse response g(t),

b(

J

)

be the weighting defined from the inverse of the colouration
threshold curve,

then the weighted autocorrelation function

N

'

gg

(

J

) is

The central maximum in

N

'

gg

(

J

) is

N

'

gg

(0). Let

J

o

be the value of

J

at which

the first side lobe maximum occurs, then audible colouration is expected
if

Support

The above discussions clearly show that generally reflections within a short time delay
from the direct sound support the direction sound, except in special occasions where a
reflection level is very high and comes in either too late (thus becomes an echo) or too
early (thus becomes colouration). The support given by the early reflections makes the
source sounds more extended and louder.

The reflections that arrive at a later delay time contributes to the reverberant part of the
room response. The main effect of the reverberant energy is to produce a background
level to the room. It can be beneficial, e.g. in music to give 'warmth' to the music, but
can also be undesirable, e.g. acting as a background noise thus reducing the
intelligibility of the signal as well as potentially causing echoes. This latter effect is in
direct opposition to the support given to the signal by the early reflections.

Hence one should distinguish between the early part of the impulse response from the
late part. Haas and Muncey's results show that the critical delay time, before which
reflections support the direct sound and after which reflections merely contribute to the
reverberation, should be in the region of 50-100ms depending on the nature of the
sound source. The usual choice is 50ms for speech and 80ms for music.

Obviously in practice there are so many reflections in a real life reflectogram that it is
impossible to examine reflections individually in any details. Hence several authors
have developed single figure objective measures for comparisons between early and
late (reverberant) energies. These measures, or parameters, can be classified into
groups, each addressing a different subjective aspects of the sound field.

Subjective Measures of the Acoustic Quality of a Room

For Speech:

Intelligibility
Level

For Music, more complex and subtle

Description:

Scale

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 14 -

(26)

(27)

Reverberance:

Live

<-------->

Dead

Clarity:

Clear

<-------->

Muddy

Loudness:

Loud

<-------->

Quiet

Influenced by visual clues, subjective
Loudness same despite lower SPL

at rear

Balance:

Warmth

<-------->

Brillance

RT at 125Hz

.

50% > at 1kHz,

RT at 250Hz

.

15% > at 1kHz

recommended

Spaciousness:

Expansive

<-------->

Restricted

Intimacy:

Intimate

<-------->

Remote

Best related to level and initial time

gap

Clarity

The most common objective parameters are:

Deutlichkeit [Thiele, Acustica 3, 1953, p.291]

D

50

is developed for speech, hence the use of 50ms as the critical delay

time. It has been shown to have very good correlation with the % scale of
Speech Intelligibility (50% D

50

.

90% Speech Intelligibility).

Clarity Index [Reichardt et al, Appl.Acoust. 7, 1974, p.243]

C

80

is developed for music, hence the use of 80ms as the critical delay

time.

C

80

= 0dB is sufficient for even fast music,

C

80

= -3dB is still tolerable.

A problem with the above two parameters is the sharp cutoff times in the definitions.
A strong reflection arriving just about the cutoff times will cause significant changes
in the parameter values depending on whether it comes before or after the cutoff, but
will cause very little subjective differences. However such situations are rare and
despite this potential problem D

50

and C

80

are still popular in architectural acoustics.

Centre Time [Kürer, Acustica 21, 1969, p.370]

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 15 -

(28)

This is basically the 'centre of gravity' of E(t). The use of continuous time
weighting ensure that the sharp cutoff problem with D

50

and C

80

will not

occur. T

c

is low for high speech intelligibility.

Other measures:

Echo degree [Niese, Acustica 11, 1961, p.199]

Signal to Noise Ratio [Lochner & Burger, Acustica 11, 1961, p.195]

The above parameters are all based on the energy time function E(t). For speech there
are two measures which are based on transmission modulation rather than E(t).

Speech Transmission Index STI

[Houtgast & Steeneken, Acustica 28, 1973, p.66; JASA 67, 1980, p.318]
Based on the modulation transfer function (MTF).

Rapid Speech Transmission Index RASTI

[Houtgast & Steeneken, Acustica 54, 1984, p.186]
Modified form of STI. Much easier to measure.

Spaciousness

The early reflections also determine the perception of arrival directions and so influence
the acoustical sensation of space.

In the early part of the impulse response human hearing is not able to locate reflection
directions separately but rather processes them into an overall impression, hence the
result is an apparent change of the feeling of space or direction of the direct sound,
depending on several conditions. It was found that

!

even with background reverberation, identical signals from loudspeakers at equal
distance from a listener but at different directions only create a 'phantom sound
source', i.e. an imaginary source at a single location', rather than a sensation of
space,

!

spatial impression can be brought about with reflections that

(i)

are mutually incoherent (reflections in real halls with many time delays,
arrival directions, and phase changes by wall impedances, are at least
partially incoherent),

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 16 -

(29)

(30)

(31)

(32)

(33)

(ii)

have time delays < 100ms and adequate intensities,

(iii)

must arrive from lateral directions.

An objective measure for spaciousness is

Early Lateral Energy Fraction [Barron M., J.Sound & Vib. 15, 1971, p.475]

where

2

is the lateral angle (with polar axis along listener's ears), and

Note that E

0-80

includes the direct sound energy while E

5-80

does not.

ELEF can be related to the subjective scale of Spaciousness by Reichardt
and Schmidt [Acustica 18, 1967, p.274]. At a music level of 70dB,

Spaciousness depends on music level. Barron [J. Sound & Vib. 77, 1981,
p.211] suggests a measure call Spatial Impression (SI) to account for the
level,

SI can be compared with Reichardt's scale directly.

Modified form of ELEF

Measurements of lateral energy are usually carried out by means of figure-
of-8 microphones, which measures p(t)

!

cos

2

. Direct squaring of the

measured pressure function therefore gives E(t)

!

cos

2

2

instead of

E(t)

!

cos

2

desired by eqn.(29). Hence it is convenient to define a modified

form of ELEF as

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 17 -

(34)

(35)

(36)

(37)

It can be shown that, in an ideal diffuse field,

and hence

Other measures:

Interaural Cross-Correlation IACC

[Damaske P. & Ando Y., Acustica 27 ,1972, p.232]
Sound arriving laterally is perceived differently at the two ears due to head
diffraction. Hence the cross-correlation between the pressure at the two
ears gives an indication of the amount of lateral energy. IACC is
developed on this principle with a time window of 100ms. It is very very
approximately related to ELEF by

Early Decay Time

The reverberation time (RT) T

60

has been, and still is, the most relied on parameter in

room acoustics because

1)

it can be measured or predicted easily with reasonable accuracy,

2)

it is usually independent of positions in a room,

3)

there is a large existing database on the T

60

of existing halls, which can be used as

invaluable comparison basis,

4)

halls of good acoustical reputation do have mid-frequency T

60

consistently falling

into a narrow range of values (for music 1.6s < T

60

< 2.2s, for speech 0.5s < T

60

<

1.2s with shorter T

60

at lower frequencies since low frequencies contribute very little

to speech),

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 18 -

(38)

(39)

5)

accuracy on T

60

estimation is not critical, a threshold of 4% or 0.1s margin can be

tolerated even in clear-cut ideal conditions [Seraphim, Acustica 8, 1958, p.280].

Problems with T

60

is that

1)

Importance of the early part of the impulse response is not addressed.

2)

In practice a decay curve is seldom a straight line with a constant decay rate. The
curve may be bent and have different decay rate at different time (e.g. if the decay
consists of many exponential decaying modes with different damping as suggested
by the wave theory).

3)

Although RT is defined over a 60dB decay, a listener can hardy be expected to be
able to listen to levels of -35dB in continuous speech or music.

Modern day measurements of RT use the decay from -5dB to -35dB and use linear
regression to determine the decay rate and then extrapolate to obtain RT over -60dB

Atal et al [Proc. of the 5th ICA, Liége 1965, G32] have shown that the initial slope (first
160ms) of a non-exponentially decay is the most significant for the subjectively
perceived 'reverberance', and for the determination of an equivalent T

60

.

Jordan [JASA 47, 1970, p.408] proposed a measure, the Early Decay Time (EDT), to
characterise the rate of sound decay in its initial portion. EDT is the time in which the
first 10dB fall of a decay process occurs, multiplied by a factor of 6 to give an
equivalent -60dB.

Level

The absolute sound pressure level in a room is highly dependent on source power and
the RT of the room. It is considered to be less important than the parameters considered
so far but is still significant in that a suitable SPL must be maintained to support the
signal - a high clarity is of no use if the SPL is too weak to be heard.

A suitable measure of level, which takes out the dependence on source power, is the
loudness level L,

where E

10m

is the direct energy (free field) at 10m from the source.

In practice E

10m

is usually determined from measurements as

where r is the distance from the measurement position to the source, and

)J

is the

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 19 -

duration of the excitation impulse.

L can vary a lot in concert halls, especially under or above balconies, where shadowing
effect may be significant.

PARAMETER VALUES IN AN IDEAL DIFFUSE FIELD

Let an impulse of total energy E

s

exists at t=0, the power of the impulse is then W =

E

s

*

(t).

Assume that an ideal diffuse field is established right at the start of the impulse, i.e. for
t

$

0, we can then use the diffuse field power balance equation

The equation can be solved by the method of Integrating Factor. For the equation

In our case r(t)=E

s

*

(t)/V and f(t)=Ac/4V = constant. Let

J

E

= 4V/Ac, then h = t/

J

E

and

Since E

*

=E

s

/V (diffuse right at t=0) at t=0, therefore the integration constant C=0, and

Hence the energy function E(t)=E

*

can be written as

where

J

E

=4V/Ac

.

T

60

/13.8 in a diffuse field, and E

o

=E

s

/V is the initial energy density.

Hence the total energy in the time period t

1

to t

2

is

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 20 -

(40)

(41)

(42)

(43)

(44)

Substituting appropriate time values into the parameter equations, one obtains,

Deutlichkeit [eqn.(26)]

Clarity [eqn.(27)]

Centre Time [eqn.(28)]

Given that

therefore

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 21 -

(45)

(46)

(47)

Early Lateral Energy Fraction [eqn.(29)]

Modified Early Lateral Energy Fraction [eqn.(33)]

It has been assumed in the above two equations for ELEF and ELEF' that E

5-80

.

E

0-80

.

Level [eqn.(38)]

Assuming a spherical source, and referring back to eqns.(8) and (9), then

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 22 -

PARAMETER VALUES IN A DIFFUSE FIELD WITH INITIAL REFLECTIONS

The diffuse energy density generated by an impulse is as given before,

This can be related to the diffuse pressure through the relationship p

2

=E

D

c

2

, hence

The direct discrete sound pressure generated by the impulse, total over the duration of
the impulse, is given by (note that in steady state p

2

=W

D

c/4

B

r

2

)

where r

D

is the distance from the source. Hence the diffuse pressure can be related to

the direct pressure at a receiver at r

D

by

Assume that the late part of the sound field (the late incident energy=p

2

/

D

c) at t

$

t

1

after

the direct sound is given by an established diffuse field, then the late energy is given
by

The early energy is given by the incoherent sum of the direct sound and early
reflections (t<t

1

),

From the ratio of the early and late energy we can determine the acoustic parameters,

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 23 -

While the ELEF is determined from the early energy only (t

1

=80ms)

and the modified

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 24 -

RANGE OF PARAMETERS IN EXISTING HALLS AND THEIR PREFERRED RANGE

The following table gives the parameters (for music) as averages over the 500Hz and
1kHz octave frequency bands. The difference limen is averaged over fast and slow
music.

Existing Range

Difference

Limen (50%)

Preferred Range

D

50

15% to 47%

[Beranek & Schultz 1965, 4 halls,

un-occupied]

(add 12% for occupied halls)

C

80

-2.9 to 2.7dB

[Tachibana 1989, European halls,

un-occupied]

-2 to 7dB (Mean 1.5dB)

[Bradley 1983, 4 halls, un-occupied]

(add 2dB for occupied)

0.67dB

[Cox, Davies

& Lam 1992]

0 to 8dB

(depends on style and

tempo. Faster music

requires higher. Slow

music can tolerate down to

-3dB)

T

c

8.6ms

[Cox, Davies

& Lam 1992]

< 140ms (Diffuse)

(i.e. Early energy better

than linearly distributed in

diffuse field)

ELEF'

0.12 to 0.19

[Bradley 1989, 10 halls]

0.05

[Cox, Davies

& Lam 1992]

As high as possible

IACC

0.22 to 0.43

[Tachibana 1989, 6 European halls]

0.17 to 0.41

[Bradley 1983]

0.075

[Cox, Davies

& Lam 1992]

EDT

Same or slightly shorter

than T

60

T

60

1.5s to 2.2s

[Cremer 1982 book, 24 halls

worldwide. British halls generally

un-reverberant]

4% or 0.1s

[Seraphim

1958]

1.6s to 2.1s

[Cremer]

1/T

60

=0.1+5.4S

T

/V

[Beranek, S

T

=total floor

area of audience]

NB. According to Cremer (p.410), a person on an upholstered chair in an audience area represents a

.

0.6m

2

absorption area. If one assumes the entire absorption is from the audience, and let n be the number of listeners,
then T

60

=0.161V/(na) => (V/n)

.

4T

60

. With a preferred T

60

of 2s, then (V/n)

.

8m

3

/listener. Hence one can

estimate the required volume for a given audience capacity to achieve reasonable acoustics.

NB. All parameters except T

60

are highly dependent on positions in a hall.

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 25 -

SOME POINTS ON HALL DESIGN

Uniformity of sound field is generally preferred. Hence diffusion should be improved
by suitably irregular hall shapes and introduction of scattering surfaces.

1)

Reverberation Time

!

Design RT to give preferred values according to the purpose of the hall (e.g. for
music 1.6s < T

60

< 2.2s, for speech 0.5s < T

60

< 1.2s with shorter T

60

at lower

frequencies since low frequencies contribute very little to speech).

!

Use absorption to adjust RT. Use selective absorption (e.g. resonant absorbers)
to adjust RT at different frequencies.

!

Use diffusers (e.g. Quadratic Residue Diffusers) to improve the diffusivity of the
hall if the hall is not naturally diffusive.

2)

Echoes, Flutter Echoes

!

Rear wall absorption to prevent echoes, esp. if rear wall is concave (focusing).

!

Irregular shapes to increase diffusion to reduce risk of flutter echoes.

3)

Provision of Early Energy

!

Increase coverage of early reflections by means of reflectors, e.g. overhead
reflectors, side wall reflectors, orchestra canopies etc.

!

Beware of colouration - change in the timbre of the original signal (e.g. reflectors
too close to audience).

!

Very important for large halls in which natural early reflections are few (e.g.
Royal Albert Hall - requires lots of overhead reflectors).

4)

Seating

!

Raked -

to improve line of sight,
to reduce seat dip attenuation.

5)

Hall Shapes

!

Shoe Box (Rectangular) Shapes

!

best because there are
(a)

no focusing,

(b)

good lateral reflections.

!

Fan Shapes

!

Preferred by architects because
of good line of sight.

!

Not good acoustically because
of lost of lateral energies (side
wall reflections tend towards
the back of hall instead of the
audience).

!

Stepped side walls to bring
lateral reflections back to the audience.

!

Reverse fan shapes get back lateral energies but restrict line of sight.

!

Curved Shapes (e.g. Royal Albert Hall - elliptical)

!

Generally should be avoided to eliminate focusing.

!

Use absorption to reduce focusing.

!

Use diffusers, reflectors etc. to mix reflection directions.

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 26 -

6)

Balconies

!

Balcony fronts can act as large reflectors to nearby audience - potential sources
of colouration. Use absorptive or scattering surfaces, e.g. put elaborate
decorations on the balcony fronts.

!

Balconies can shadow the audience underneath - lost of both early and late
energies. Hence balconies should not be too low.

7)

Interferences

!

At high frequencies can be caused by diffractions over stage, balcony fronts etc.,
and by grazing reflections over hard surfaces. Such interferences are usually very
localized and should not be serious if the floor is carpeted.

!

At low frequencies mostly appear as seat dip attenuation - loss of bass. No
compliant so far - must be accepted.

!

Can be masked by providing more non-grazing reflections.

Methods for investigation

Point (1)

!

concerns the entire, and in particular the late part of the impulse response,

!

hence should use the diffuse field approach to investigate.

Points (2) to (6)

!

concerns the early part of the impulse response,

!

hence should use the geometrical approach to investigate.

Point (7)

!

requires wave theory or other exact theories to investigate interferences, difficult.

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 27 -

DISCUSSION TOPICS

!

General need to assess the acoustics of a hall before the hall is built.

!

Simple calculations can only gives estimates of RT (T

60

). Other parameters require

more elaborate predictive methods.

Physical Scale Modelling

!

Most established.

!

An experimental method based on acoustical similarity (time and dimensions
normalized to wavelength).

!

Let s be a scale factor. Denote scaled quantities by the subscript m.

lengths:

l

m

= l/s

time:

t

m

= l

m

/c

m

= l/c

m

s = ct/c

m

s = (c/c

m

s)t

wavelengths and frequencies:

8

m

=

8

/s

f

m

= c

m

/

8

m

= c

m

s/

8

= (c

m

s/c)f

The instantaneous pressure remains the same. Hence acoustic measurements made
in the physical model can be related back to the original hall by proper scaling.

Note that media other than air can be used in the modelling.

Difficulties with physical modelling are

(i)

Frequency dependence of absorption (and wall diffusion) has to match the
original.

(ii)

Air absorption is much higher at the higher scaled frequencies. The
increase in air absorption is not linear, hence numerical compensation has
to be made, or a medium which has very low absorption (e.g. nitrogen) has
to be used. Neither corrective methods is perfect.

(iii)

Directivity of source and receiver are likely to be large at the scaled
frequencies. Can use spark source and 1/8" microphone to reduce
directivity, but sensitivity will generally be sacrificed.

(iv)

Special high speed data acquisition equipment is need (e.g. 1:50 scale
modelling requires a sampling rate of at least 150kHz to cover the original
1kHz octave band).

(v)

Time consuming to get details and to modifiy models.

Computer Modelling

!

Theory, which is based on the geometrical approach, was developed long time ago.

!

Only widely used recently as a result of the rapid increase of desktop computing

AEOF3/AEOF4 Acoustics of Enclosed Spaces © Dr. Y.W. Lam 1995

- Page 28 -

power.

!

Ray Tracing Method

!

Simple implementation of the geometrical room acoustics approach by tracing
incoherent energy rays around the hall.

!

Easy to program.

!

Have problems of large number of rays, divergence of rays, and reception
volume around the receiver.

!

Have problem of diffuse wall reflections.

!

Hybrid Ray Tracing/Image Method

!

More recent development. Trace rays to find image sources then use the image
sources to calculate the sound field. Less rays required.

!

No problems of ray divergence or reception volume.

!

Have problem of image visibility - checked by time consuming 'backtracing'.

!

More difficult to program, not much faster to run than the simple ray tracing, but
more accurate.

!

Number of images required in the calculation of the later part of the impulse
response can be reduced by adopting a combined geometrical/diffuse approach,
restricting the exact image source generation to, say, the 5th order images.

!

Have problem of diffuse wall reflections.

!

Have the potential of including phase information - necessary for computerized
auralization.

Diffuse wall reflection is a problem in both computer modelling approaches, but can
be solved by either randomizing the reflection directions according to a diffuse
coefficient, or by taking energy out from the specular reflection into a diffuse energy
pool.

REFERENCES

1.

Kuttruff H., Room Acoustics, 3rd Ed. 1991, Elseiver Science Publishers Ltd., Lodon.

2.

Cremer L. and Müller H.A., Principles and Applications of Room Acoustics Vol.1, 1982,
Translated by Schultz T.J., Applied Science, London.