Project Number HU-DGW-9495

Acoustical Analysis of Spaulding Recital Hall

An Interactive Qualifying Project Report Submitted to the Faculty

of WORCESTER POLYTECHNIC INSTITUTE in partial fulfillment of the requirements for the

Degree of Bachelor of Science by

__________________________ __________________________ Michael J. Andrews Michael V. Corbin __________________________ __________________________ Andrew F. David Kyle T. Warren

May 5, 1994

Approved by:

________________________________ Professor Douglas G. Weeks, Advisor

________________________________

Professor Fredrick Bianchi, Co-Advisor

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Abstract

This IQP’s objectives were to investigate the bothersome nature of performing

and listening to music in Spaulding Recital Hall and to suggest improvements and areas

of further study. This research was conducted through impulse response testing,

resonance testing and computer simulations. The objectives were met and

recommendations were made to install a resonant-cavity absorber designed to control

modes that existed near 250 Hz and 500 Hz whose surface would provide adequate

diffusion and proper absorption for all frequencies.

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Table of Contents

ABSTRACT.......................................................................................................... 2

1. INTRODUCTION.............................................................................................. 1

2. LITERATURE REVIEW.................................................................................... 4

2.1 Physics of Sound .................................................................................................................................4

2.2 Basic Acoustics ..................................................................................................................................10

2.3 Music Characteristics.......................................................................................................................13

2.4 Classification of Acoustic Measurements .......................................................................................17

2.5 Acoustic Architecture .......................................................................................................................20

3. PROCEDURE ................................................................................................ 29

3.1 References and Observations...........................................................................................................29

3.2 MLSSA ..............................................................................................................................................30

3.3 ODEON..............................................................................................................................................36

3.4 Resonance Testing ............................................................................................................................38

3.5 Inter-Aural Cross Correlation.........................................................................................................39

3.6 Tests of Hypotheses...........................................................................................................................40

4. EXPERIMENTAL RESULTS.......................................................................... 42

4.1 MLSSA Testing.................................................................................................................................42

4.2 ODEON Testing ................................................................................................................................57

4.3 Resonance Testing ............................................................................................................................61

4.4 Inter Aural Cross Correlation ........................................................................................................63

5. EXPERIMENTAL DATA ANALYSIS AND CONCLUSIONS.......................... 67

5.1 Acoustical Shortcomings Inherent to Each Group ........................................................................67

5.2 Acoustical Shortcomings Inherent to Spaulding Recital Hall.......................................................70

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6. FINAL TESTING ANALYSIS, CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE STUDY ....................................................................................... 81

6.1 Minor Changes..................................................................................................................................81

6.2 Major Changes..................................................................................................................................87

6.3 Correlations.......................................................................................................................................93

6.4 Recommendations for Future Study ...............................................................................................94

APPENDIX A: OBSERVATION FORMS ........................................................... 97

APPENDIX B: COMPLETED OBSERVATION FORMS.................................... 98

APPENDIX C: MLSSA..................................................................................... 105

APPENDIX D: ODEON .................................................................................... 111

Creating A Model .................................................................................................................................111

Theoretical Considerations ..................................................................................................................115

Calculations...........................................................................................................................................116

Conclusion .............................................................................................................................................122

APPENDIX E: ODEON SURFACE FILE FOR SPAULDING RECITAL HALL 123

Reciever List..........................................................................................................................................123

Source List.............................................................................................................................................123

Surface File............................................................................................................................................124

APPENDIX F: RESONANCE PREDICTIONS.................................................. 136

APPENDIX G: RESONANCE TESTING APPARATUS................................... 139

APPENDIX H: CYLINDRICAL ABSORBER DESIGN ..................................... 140

APPENDIX I: ATTEMPTED DESIGN OF A DOUBLE-SIDED HEMHOLTZ RESONATOR................................................................................................... 143

APPENDIX J: INTERAURAL CROSS CORRELATION .................................. 147

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APPENDIX K: SLAT ABSORBER DESIGN .................................................... 151

BIBLIOGRAPHY.............................................................................................. 155

ACKNOWLEDGEMENTS ................................................................................ 157

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1. Introduction Problem statement:

The acoustical qualities of Spaulding Recital Hall do not provide optimum live

performance conditions for many small music ensembles. With the exception of the

Great Hall of Alden, this hall is the only other large recital space on campus. Therefore,

it is forced to accommodate all of the small instrumental groups present at Worcester

Polytechnic Institute. As participants in these groups, it was decided to address this

problem. The goals of this IQP were as follows:

1. Identification of the hall’s acoustical shortcomings for each of the groups.

Because the focus of this project was to address the problem of live performance

conditions in Spaulding Recital Hall, it follows that the analysis of the hall reflected both

“rehearsal” and “live-performance” conditions; the primary distinction between the two

being the presence of an audience. Also, to investigate the hall’s acoustical shortcomings

for each of the above groups in a live performance situation, it was necessary to

distinguish between the problems that are inherent to the hall from the problems which

are inherent to each group. In order to categorize the problems in this manner (hall versus

group), it was necessary to generate both qualitative and quantitative sets of acoustical

data. Quantitative measurements of the sound characteristics of Spaulding Recital Hall

were made using the Maximum Length Sequence System Analyzer (MLSSA).

Specifically, MLSSA is a computer driven tool that measures the impulse response of a

linear time-invariant system. Also, we performed resonance tests on the hall, using an

amplified frequency generator. Qualitative aural observations were made for each

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musical group by members of the IQP team and the groups’ conductors. Through

correlation of both data sets, insight was gained into the nature of the hall’s acoustical

shortcomings for each of the ensembles. In an attempt to be thorough in the

investigations, the IQP made use of the following on-campus performance groups: Jazz

Ensemble, Medwin String Ensemble, Brass Ensemble, and the Woodwind Ensemble. It

is felt that these groups were not only representative of a wide range of musical styles, but

also demonstrated these styles in the context of a small ensemble.

2. Investigation of potential solutions for identified problems.

It was the intent of this IQP to investigate possible improvements that can be

made to Spaulding Recital Hall. Upon classification of the acoustic problems identified

in section 1 as being either “hall” or “group” related, it was possible to formulate

hypotheses concerning the acoustical improvements that can be made to the hall.

Suggestions for improvement were based on the correlative findings of the two data sets

of section 1. As an aid, an acoustic model of Spaulding Recital Hall was created using

the computer program Odeon. This model provided the opportunity to test hypotheses in

a simulated environment, allowing for more educated decisions concerning

improvements. Through this modeling process, a final set of suggested changes was

produced.

In an attempt to examine one possible solution to the acoustical shortcomings of

Spaulding Recital Hall, one type of sound absorbing device was designed and

constructed. The effects of this absorber were qualitatively tested in the hall using a

variety of musical instruments. The instruments selected for this test were chosen

because their individual frequency ranges fell within the room’s identified problem areas.

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3. Areas for further study.

While our investigations proved conclusive, it was clear that the need for further

study remains. As the initiators of this IQP, it is felt that the established knowledge base

will serve as a foundation for future projects.

In closing, this IQP fulfilled the objectives of the degree requirements by

benefiting the WPI community in the investigation of sound quality in the second largest

musical performance hall on campus. Because of its use academically, the

implementation of this report’s suggested acoustical alterations will provide both teacher

and student with an improved learning environment. By making this hall more

accommodating, it will be possible for both audiences and musicians to enjoy a more

diverse range of music in a live performance condition.

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2. Literature Review

A number of periodicals, journals and books were investigated for information on

topics ranging from acoustical architecture to the physics of music. Also, information

came to us in the form of correspondences with members of the Music Division faculty at

WPI and Professor Richard Campbell of the Electrical Engineering department. In the

following document a quick reference system is created, which will provide the reader

with a means to investigate the research important to the project. A brief discussion of

each topic will be accompanied by a list of the sources used for the research. The topics

are as follows:

• 2.1 Physics of Sound

• 2.2 Basic Acoustics

• 2.3 Music Characteristics

• 2.4 Classification of Acoustical Measurements

• 2.5 Acoustical Architecture

2.1 Physics of Sound To carry out the acoustical analysis of Spaulding Recital Hall, it was important

that all team members have a basic knowledge of sound. This understanding will enable

the IQP team to make the appropriate measurements of the sound in the hall and to aid in

making acoustic modifications.

Of particular benefit towards an understanding of sound is Basic Acoustics,

written by Donald E. Hall. While Basic Acoustics deals mainly with recording

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techniques, microphone construction, and the transfer of sound to recording media via

electrical transduction, it does contain a good description and definition of sound.

“Sound is a wave phenomenon; that is, each little parcel of air (or water, or concrete, or whatever else carries the wave) vibrates in some fashion and passes on the disturbance to its neighbors. But while this disturbance carries both information and energy to distance places, each bit of air remains always in the vicinity of its original position. In a gas or liquid the local vibration is always parallel to the direction of travel; so sound waves are classified as longitudinal waves” (Hall, p. 3).

Because sound is a wave, the laws and phenomena that apply to wave behavior are used

to describe it. It is interesting to note, that while sound waves are longitudinal, it is

possible to quantify their motion using equations governing transverse waves. In a

transverse wave, the oscillations forming the wave are perpendicular to the direction of

propagation. However, in a longitudinal wave, the oscillations of the medium forming

the wave are parallel to the direction of propagation (Berg-Stork, p. 21). An example of a

transverse wave can be seen in figure 2.1.1.

Figure 2. 1.1 A transverse wave.

In Physics of Sound , written by Richard E. Berg and David G. Stork, the nonscientist is

presented with an excellent discussion of transverse and longitudinal wave motion, in

addition to a wide range of topics in acoustics and music. The entire discussion of wave

motion is covered with as little math as possible, none of which exceeds the level of high

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school algebra. It is for this reason that chapters one through four of Physics of Sound

are used as the foundation for the following discussion of the physics of sound.

Because sound exactly repeats itself after successive time intervals, its motion is

referred to as periodic. To quantify the motion of sound, the main concern is with the

frequency at which this periodicity is exhibited, and how this frequency corresponds to

the wave's velocity (rate of propagation of the wave). Knowing that wave frequency is

measured in hertz (number of cycles per second), we can relate the period to frequency

through the following equation:

fT

Tf

= ⇒ =1 1 Equation 2.1.1

where: f is the frequency (cycles/second, or Hz.) and T is the period (seconds)

In figure 2.1.1, it is seen that the wave (or medium; air in the case of sound) has been

displaced a maximum distance perpendicular to the direction of propagation during the

period. This distance is the wave's amplitude (A). It can also be observed from figure

2.1.1 that in a time interval of one period (T), the wave has traveled a distance of one

wavelength (λ). The speed of propagation of the wave (v) is then equal to the distance

traveled divided by the time interval.

vT

v f= ⇒ = ⋅λ

λ Equation 2.1.2

Because sound propagates with a constant speed in air, it can be seen from equation 2 that

wavelength is inversely proportional to frequency. That is, low frequency waves will

have very large wavelengths, and high frequency waves will have very small

wavelengths. This relationship between frequency and wavelength will be of significant

importance concerning the topic of acoustic architecture.

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Another measurable quality of sound is its strength or intensity. The strength of

sound is measured on a logarithmic scale called sound level. Sound level measurements

can be made by relating either the intensity (power/area) or pressure change (force/area)

of the sound to a set reference. Respectively, these are called the sound intensity level

(SIL) and the sound pressure level (SPL). The unit of measurement for these scales is the

Bel, or more commonly, the decibel (one tenth of a Bel).

With the description of a single wave's motion in place, it is necessary to

investigate the effects that additional waves impose on each other. The law governing the

coexistence of waves is the law of superposition:

“The existence of one wave does not affect the existence or properties of another wave, even if they are in the same place at the same time.” (Berg-Stork, p. 30)

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The law of superposition states that waves are added together algebraically. The net wave

is equivalent to the sum of the displacements of all the waves present at the same place

and at the same time. The superposition principle is useful in describing the effects of

multiple waves occurring at the same time. A special case of two waves occurring at the

same time is when the waves are identical in amplitude, yet moving in opposite

directions. The result is a standing wave (one that appears stationary) of the same

wavelength as the two component waves and with an amplitude twice that of the original

component wave. Shown in figure 2.1.2 is a standing wave with an amplitude of two and

one of its component waves with amplitude one. The points of zero amplitude are

referred to as nodes.

Figure 2.1. 2 A standing transverse wave.

Standing waves are produced in a medium bounded by harder, reflective, parallel

surfaces. These waves exist at frequencies found at integral multiples of a fundamental

frequency called harmonics. The fundamental frequency corresponds to the half

wavelength span between the parallel surfaces. One can imagine the undesired acoustic

effects standing waves would have in a room. The nodes would effectively be dead spots

with no sound, where the points of double amplitude would correspond to extreme

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loudness. For those reasons, a major goal in acoustic architecture is to avoid situations

which produce standing waves.

Because sound decays as it propagates, it is important to define the manner in

which this decay occurs. The inverse square law tells exactly how the intensity of a

sound wave decreases as the distance between the source and the observer increases. For

a wave confined to two dimensions, the intensity (I) of the wave is inversely proportional

to the distance (r) between the source and the observer. Mathematically, this is:

Ir

∝ 1 Equation 2.1.3

An example of a two-dimensional wave would be the ripples caused by a stone thrown

into a pool. Since sound travels in three dimensions, the inverse square law states that

intensity is inversely proportional to the square of the distance between the source and the

observer. This is expressed as:

Ir

∝ 12

Equation 2.1.4

An example of a propagating three-dimensional wave would be an expanding balloon.

Since the surface area of a sphere is directly proportional to the square of its radius, it

follows that the intensity decreases by 1/r2. The inverse square law says nothing about

the losses due to sound being absorbed or about the frictional losses resulting from the

motion of air molecules. Nonetheless, the inverse square law plays a large role in the

determination of sound decay in the context of acoustic architecture.

The reflection of sound waves off a surface is characterized by the angle of the

incident wave (i), being the same as the angle of the reflected wave (r). This is shown in

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figure 2.1.3. A complex case of sound reflection is the focusing of the reflected waves by

a concave reflector.

Figure 2.1. 3 A reflected wave.

This creates a situation which is undesirable for listening. The focused sound

corresponds to extreme loudness, while areas in the vicinity of the focal point would

seem quiet by comparison. It follows that another goal in the design of a hall is to avoid

curved, reflective surfaces which approximate this concave shape.

2.2 Basic Acoustics

The following section is intended to familiarize the reader with four important

concepts in acoustics: resonance, diffusion, absorption and reverberation. Resonance

occurs in halls when certain frequencies excite standing waves between any of the

surfaces. Sound diffuses when obstacles in its path cause the sound to be scattered rather

than simply reflected. This minimizes standing waves and contributes to a rich, full tone.

When sound strikes a material, it is either absorbed or reflected; the measure of which is

called the absorption coefficient. Reverberation provides a means to describe the overall

manner in which the sound decays in the room. It is often treated as the most important

measure of a hall’s acoustics.

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In a mid-sized hall, resonance is expected to play a part in the observed acoustics

of the room. From the earlier discussion on standing waves (Physics of Sound), it was

noted that standing waves are produced in a medium bounded by a harder, reflective

material and that they exist at frequencies found at integral multiples of a fundamental

frequency called harmonics. The fundamental frequency corresponds to the half

wavelength span between the two surfaces. For example, examine figure 2.2.1 shown

below; this diagram depicts the fundamental frequency and three harmonics in a bounded

material; in this case, the air inside of a room or small studio.

Figure 2. 2.1 A fundamental frequency and its harmonics.

The diagram in figure 2.2.1 shows two walls separated by a distance of six meters,

a situation that might be found in a small recording studio. Standing waves are shown to

exist at integral multiples of the fundamental frequency, with a half wavelength of six

meters. It is often useful to refer to the frequency of a wave, rather than the wavelength;

therefore, a calculation for frequency is in order. Frequency is a function of both the

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speed of sound in air and the wavelength of the wave it describes. Noting that sound

travels at approximately 344.5 meters/second in air, the calculation of frequency is

simply:

f =

v

λ=

344.5 meters / sec

12 meters= 28.7 Hz Equation 2.2.1

In this case there is a resonance at approximately 29 Hz between two of the walls.

The artist who is forced to paint on a previously colored canvas is in a similar

predicament as the musician who is required to perform in a room with strong

resonances. For the artist, certain colors will tend to be accentuated; and for the

musician, certain notes will be amplified. Any musician who has played in a room with

pronounced resonances can testify to its ability to scar an otherwise perfect performance.

Fortunately, methods exist for identifying and correcting these problems. These

procedures are discussed in the section on Acoustic Architecture.

One of the qualities of a good hall is that the reflected sound, the sound that does

not reach the listener directly from the stage, is diffused so that no particular reflections

are favored. In Our Acoustic Environment, Mr. White states,

“A diffuse field is one in which a large number of reflected or diffracted waves combine to make the sound energy reasonably uniform throughout a space” (White, p. 83).

Therefore, a room with a very diffuse sound field has no resonances and bears no

distinguishable echoes. On the other hand, a room without a diffuse field tends to be dry

sounding and has many problems with flutter echoes and standing waves. In many ways,

acoustic architecture is the science of creating a diffuse sound field.

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Every material used to construct rooms both absorbs and reflects sound to some

degree. This relationship is quantified in Our Acoustic Environment as:

“The reflection coefficient, r, is defined as the ratio of the amplitude of the reflected wave to the amplitude of the incident wave. The fraction of the energy that is absorbed when a sound is incident upon a material is called [the] sound absorption coefficient, α, of the material” (White, p. 92-93).

This is further quantified by the expression:

α =1 − r 2 Equation 2.2.2

The absorption coefficients of various materials will play a vital role in latter parts of this

project and be discussed in the Procedure.

In the study of acoustics, much attention is paid to the manner in which sound

dissipates. Of particular concern is the time it takes sound to decrease 60 decibels, or to

one millionth of its original intensity. This quantity is defined as reverberation time or

decay time and is a deciding factor of a room’s strengths and weaknesses. Reverberation

time is a function of room volume, total area and absorption of the surfaces, and the

frequency of the sound wave. Mr. Beranek comments on reverberation in Music,

Acoustics & Architecture:

“In acoustics, reverberation is defined as the sound that persists in a room after the tone that created it is stopped. The length of time it takes for the level of the sound to decay by 60 decibels is defined as the reverberation time” (Beranek, p. 29).

2.3 Music Characteristics In Richard E. Berg and David G. Stork’s The Physics of Sound and Leo L.

Beranek’s Music, Acoustics, and Architecture, there is a vast amount of material

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discussing the common terminology for describing room acoustics. The following is a

summary of some of the important ideas discussed in both of these books.

For each type of musical group, there is a certain quality of sound that is desired.

This quality is often based on the conductor’s personal taste as well as the style of music

being played. The essence of each group’s sound, however, can be described by the

following properties: liveness, intimacy, fullness, clarity, warmth, brilliance, texture,

blend, and ensemble.

Liveness is used to describe a room’s reverberation time. The more “live” a

room sounds the longer the reverberation time. Every style of music requires a different

amount of liveness. Baroque music requires a very small reverberation time. Romantic

music on the other hand, should have a reverberation time around two seconds, according

to authors Berg and Stork. Much of this depends on the nature of the particular musical

style. Articulate music requires short reverberation times in order to hear distinct

syncopated rhythms. Music with many sustained chords requires a long reverberation

time to create a blend of sound. A room is regarded as “dead” if there isn’t much sound

reflection.

In Berg and Stork’s, The Physics of Music, intimacy is said to be “achieved

whenever the first reflected sound reaches the listener less than about 20 ms after the

direct sound” (Berg-Stork, p. 206). This allows the audience to feel as if they are

listening to the performance in a small hall and are surrounded by the musicians’ sound.

Baroque music is often played in intimate conditions such as these.

If the reflected sound intensity level is similar to the intensity level of the direct

sound, a room is considered to have fullness. Much like other acoustical properties,

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fullness is related to reverberation. Berg and Stork comment: “In general, greater

fullness implies a longer reverberation time” (Berg-Stork, p. 206). A “full” room is often

desired for slow music from the romantic period.

The opposite of fullness is clarity. In listening to speech, early Classical, or

Baroque music, clarity is necessary so that every word of a sentence or nuance of a piece

is audible. A room that has good clarity also lends itself to faster musical pieces, so that

notes are distinct and don’t run into each other. In most cases, improving clarity involves

shortening the reverberation time.

Individual frequency bands behave differently in a room, often resulting in

contrasting reverberation times. When the intensity of low frequency reverberations is

greater than that of the high frequencies, a room has warmth. However, if this difference

in intensity becomes too great, the room will sound “muddy”. When this difference is

less pronounced, it is called brilliance. The room could develop a continuos high-pitched

ringing if the high frequency intensity becomes greater than the low frequency intensity.

Leo L. Beranek, in Music, Acoustics, and Architecture, describes texture as “the

subjective impression created in the mind of the listener by the pattern in which the

sequence of sound reflections arrives at the listener’s ears” (Beranek, p. 69). A room

that has good texture usually has five reflections within 60 ms of the direct sound

(Beranek p. 70). Each successive reflection should also be of lesser intensity than the

previous for the decay to be linear.

Regardless of the style of music, it is important for everyone to hear the same

mixture of sound. This is called blend. In a room with good blend, sound must be mixed

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as it is projected from the performance area. The room should also have the appropriate

types of diffusing surfaces so the entire audience hears the mixed sound.

One of the most important characteristics of a room’s sound is ensemble, the

performers’ ability to hear each other. To achieve this, the reverberation time in the stage

area must not be longer than the fastest notes to be played. In essence, the performance

area should be acoustically identical to the audience area.

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2.4 Classification of Acoustic Measurements There are many different factors that are involved in the architectural design of an

auditorium. Some of these are room dimensions, external noise levels, and sound control.

Since this project deals with a pre-existing auditorium, the only factor that can be

changed is the sound within the room. The focus of this project is to examine three major

characteristics of the acoustics of Spaulding Recital Hall: clarity, decay, and

reverberation. This section discusses the numerical calculations for each of those

attributes.

As mentioned before, clarity is the ability to discern one note from another. This

property is dependent upon the overall strength of sound. More importantly, however, it

depends on a strong direct signal. The less competition there is between the direct sound

and continuing reverberation, the easier the music will be to understand.

An objective measurement which correlates with clarity is obtained by taking a

ratio of the early to late sound strength. Using sophisticated analytical devices, it is

possible to measure the magnitude of sound energy that arrives before and after a certain

time t = τ, where time t = 0 is the arrival time of the first direct signal from an impulsive

source. The ratio

CE t

E t80 10

0=

< <>

log( )

( )

ττ

Equation 2.4.1

measures the relative prominence of the early sound (Hall, p. 188). For this project, E is

the energy contained in the signal and τ = 80 ms. This means that a value of 0 < C80 < 2

will result in acceptable levels of clarity. A value of C80 > 2 denotes a room with too

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much clarity making it undesirable for music, and a value of C80 < 0 corresponds to a

significant lack of clarity.

Decay, or smoothness as it is sometimes referred, is the manner and time in which

sound dies away to an inaudible level. Ideally, sound should dissipate exponentially.

This exponential decay appears linear on a logarithmic graph. Unfortunately, there are

many reasons why it may not. One reason is the presence of a strong secondary

reflection. If a large hard wall produces a reflection that is significantly stronger than

preceding ones, it can cause an echo effect. Another way that sound may be “rough” is

for there to be excessive periods of time between early reflections. As long as the first

reflection arrives at the listener’s ears sooner than 30 to 40 ms after the direct sound and

every reflection is followed by another within a similar time period, all the reflections up

to 80 ms or so will have the psychological effect of being part of the direct sound. Any

gap of more than 40 ms between one component and the next will tend to ruin this

desirable effect (Hall, p. 192).

The numerical value that corresponds to smoothness is known as early decay time

(EDT). This number is calculated by measuring the amount of time it takes for the

sound-pressure level to decrease by a factor of 10 dB. This is given by the formula

EDTdB

M=

−10 Equation 2.4.2

where M is the slope of the decay curve. This value will properly demonstrate whether

the time periods between early reflections are too large.

The final acoustic characteristic to be examined, reverberation, is merely an

offshoot of decay. It is defined as the prolongation of sound after the source ceases to

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emit energy (Parker, p. 175). A certain amount of reverberation is pleasurable in music;

however, an excessive amount can destroy the acoustical properties of an otherwise

suitable auditorium.

Reverberation time (RT-20) is given as the amount of time required for the

sound-pressure level to decrease by one-millionth, or 60 dB, of its original intensity. The

following formula is given to calculate the reverberation time:

RTdB

M− = −20 20 Equation 2.4.3

where M is the slope of the decay curve for the first 20 decibels. Shown in figure 2.4.1 is

a depiction of (RT-20).

Figure 2.4.1: A graphical representation of RT-20.

What is the recommended length of time for reverberation, in order for it to be

pleasing? The answer is unique to the listener and to the type of music being performed.

Each style of music has its own sense of warmth and color which comes from

reverberation. Some composers have even gone as far as creating pieces to be played

specifically in certain halls, based on the hall’s unique acoustical qualities. Reverberation

is by far the most subjective value that needs to be examined. For this project, the expert

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opinions of the directors of each ensemble will be used in determining the proper

reverberation times.

2.5 Acoustic Architecture While being many things, the art of acoustic architecture is certainly not an exact

science. The following quote, taken from Professor Richard Campbell’s introduction to

the reprint of the article Annals of Architecture - A Better Sound is adequate evidence of

this.

“...but I hope that the next few thousand [students] will appreciate the blend of art and science, experience and luck, knowledge and conviction which couples an engineering masterpiece [the reconstruction of Avery Fisher Hall] to the people who, immersed within it, are pleased with its workings in every way...”

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This article, originally appearing in the New Yorker Magazine, narrates the trials and

tribulations of the renovation of Avery Fisher Hall (in Lincoln Center) by Cyril M. Harris,

professor at Columbia University. In reading this article, one learns of the previous

failure encountered in an attempted renovation by renowned acoustic architect, Leo L.

Beranek. Beranek, author of the book Music, Acoustics and Architecture, demonstrated

the inexact nature of acoustic architecture through the misapplication of acoustic theory,

creating a hall which Harris would later refer to as “dull, lifeless and lacking sufficient

bass”. Ultimately, Harris determined that the shape of the hall was problematic,

contributing to the lack of sound diffusion and transmission of low frequencies. One of

the major points of the article was to introduce the concept of the sound decay curve.

Harris defines the ideal sound decay curve as an approximation of a straight line having a

nearly constant slope, shown in figure 2.5.1.

Figure 2.5.1: Ideal decay curve.

Unfortunately the decay curve in Avery Fisher hall was far from ideal. The following,

taken from the article, describes the problematic situation in Avery Fisher Hall:

“...and so the decay curve’s fluctuations were irregular instead of smooth; moreover the initial decay rate was too fast, resulting in a double slope...”

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A double sloped decay curve, shown in figure 2.5.2, tricks the ear into believing that there

is a short decay time (corresponding to slope 1), indicating a dead room. Even though the

decay time, in this case, is two seconds, it is not perceived as such. This lead to the

conclusion that it is not only the decay time but the shape of the decay curve that is

important.

Figure 2.5.2: A double-sloped decay curve.

The ability to temporarily disregard the shape of the decay curve has its merits as

well. In the graph in figure 2.5.3, the x-axis is formatted logarithmically in octave bands

and the y-axis represents reverberation time in seconds. Octave bands are a convenient

acoustical unit of measure that divides frequency ranges into octaves; in fact, musicians

may note that 250Hz is the octave above 125Hz, and 500Hz the octave above that, etc.

By viewing this two-dimensional plot, it can be clearly shown that a problem exists in the

250Hz region, where there is a discontinuity in the gentle slope of the solid line. This

discontinuity corresponds to a sound field which is lacking in diffusitivity, specifically in

the 250Hz octave band for the case shown. A more acceptable, “flattened” curve,

23

corresponding to a diffuse sound field, is represented by the dotted line (Everest, 209). A

more acceptable curve is represented by the dotted line. Data presented in this manner is

easier to comprehend, avoiding the tedium of interpreting three-dimensional graphs.

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

125 250 500 1000 2000 4000

Frequency (Hz)

Rev

erb

erat

ion

Tim

e (s

)

Undesirable

Desirable

Figure 2.5.3: Reverberation curves with respect to frequency.

Throughout this report, graphs such as Figure 2.5.3 will be used to show early

decay time (EDT), reverberation time (RT-20), and clarity (C80). EDT represents the

time required for the sound to decay 10dB in seconds; it provides a glimpse of the initial

trend of the decay curve. RT-20 is a measurement of reverberation time, and represents

the time required for the sound to decay 20dB. C80 yields a number that represents the

‘distinctness’, ‘sharpness’ or ‘discernability’ of the tone. Acceptable clarity values exist

between 0 and 2. If C80 is too high, any music played in the room will suffer from being

too clear, lacking a full sound; on the other hand, if C80 is negative, the music will

24

become muddled. In table 2.5.1 below is a list of reasonable values for these important

units of measure.

Unit of measure Range Comment Early Decay Time (EDT) 1.5s Slow initial decay 0.5s Quick initial decay Reverberation Time (RT-20) 2.0s Slowly decaying 0.5s Quickly decaying Clarity (C80) 2 Individual sounds very discernable 0 Individual sounds not easily discernable

Table 2.5.1 A summarization of numerical values and their corresponding aural effects for early decay time, reverberation time, and clarity.

From the discussion of Basic Acoustics, it is known that room volume, surface

areas and their absorption, and the frequency of the sound waves all affect reverberation

time. Of particular concern is the size of the waves, or wavelength, with respect to the

size of the diffusing surfaces.

A surface’s size must be greater than the wavelength of the sound that hits it for

the surface to have any effect on the wave. The wave’s intensity, along with the material

properties of the surface, will determine how much of the intensity will be absorbed into,

or reflected off the surface. Problems can also arise from incorrect placement of

reflectors, which leads to poorly distributed sound. Concave surfaces produce focal

points where the sound is much louder than in the surrounding region (Stork, p. 209). In

contrast, convex surfaces tend to be effective in diffusing sound evenly across a large

area. Other problems can originate from structures like columns and balconies which

upset the distribution of sound. Sound is forced to diffract, or travel around these objects,

creating dead spots, or shadows, where the sound is nonexistent.

25

An additional problem for small rooms is resonance. As discussed previously,

resonance is a series of standing waves that are created between surfaces in the room.

Unfortunately, rooms have more than two walls, between which standing waves can be

produced. In fact, resonance, or modes of vibration, can develop between any of the

walls. Values called eigentones are the frequencies (f) that tend to stand out in a room

because of their slower decay rate caused by resonance. The following equation describes

the existence of these eigentones in a room:

f

cn

l

n

l

n

lx

x

y

y

z

z=

×

+

+

2 2 2

2 Equation 2.5.1

where c is the velocity of sound through air in meters per second, and lx , ly , and lz are

the dimensions of the room, in meters. The symbols nx , ny , and nz refer to waves

propagating in the directions of width, length, and height respectively, and are used to

categorize the types of eigentones in the following manner:

26

a. “Axial” eigenfrequencies in which two n’s = 0; that is, waves are parallel to a

room axis and only two walls are intercepted (one-dimensional).

b. “Tangential” eigenfrequencies in which one n = 0; that is, waves touch four

room boundaries but are parallel to the two other boundaries (two-

dimensional).

c. “Oblique” eigenfrequencies in which no n = 0; that is, waves progress so as to

intercept all six room boundaries (three-dimensional).

Figure 2.5.4: Axial, tangential, and oblique modes of vibration.

Integral partials in the harmonic series can be accounted for by setting nx, ny , or nz equal

to integer values greater than one. Figure 2.5.4 shows the axial, tangential, and oblique

modes of vibration for two harmonics. In brief, axial modes are one-dimensional and

involve two walls, tangential modes are two-dimensional and involve four walls, and

oblique modes are three-dimensional and involve six walls. For a room that is 6 meters

on a side, table 2.5.2 will result from an application of the equation above:

27

Harmonic Mode of Vibration Type (nx, ny, nz) Frequency

Fundamental Axial (1,0,0) 28.7

Fundamental Tangential (1,1,0) 40.6

Fundamental Oblique (1,1,1) 49.7

2nd Axial (2,0,0) 57.4

2nd Tangential (2,1,0) 64.2

2nd Tangential (2,2,0) 81.2

2nd Oblique (2,1,1) 70.3

2nd Oblique (2,2,1) 86.1

2nd Oblique (2,2,2) 99.4

3rd Axial (3,0,0) 86.1

3rd Tangential (3,3,0) 121.8

3rd Oblique (3,3,3) 149.2

Table 2.5.2: An example of axial modes and their associated frequencies.

Table 2.5.2 serves as a guideline for the “problem frequencies” that may be encountered

in this room. Stephens’ Acoustics and Vibrational Physics outlines the following

potential problem:

Degeneracy: this refers to two or more different modes (i.e. different combinations of nx, ny, nz values) which have the same resonant frequency and in consequence of this degeneracy there will be a concentration of acoustic energy in these frequencies. (Stephens’, p. 405)

28

And goes on to note a good solution: To eliminate the effects, or at least to minimize them, the walls should be

draped with highly absorbent material, which has a suitable frequency characteristic. (Stephens’, p. 405)

Examination of the table shows that there is a potential problem frequency at 86.1 Hz. It

is therefore advisable that material that is absorbent at that frequency be placed in the

room so that the resonance is less pronounced.

In summary, a list of important qualifications required to achieve excellent sound

in a room or hall has been created:

1. There must be a reasonably short initial time-delay gap

(of less than about 20 ms). (Beranek, p. 418)

2. A reverberation time that varies according to the type of music performed in

the room.

3. A smooth decay curve that offers no echo.

4. Minimal resonance to avoid amplifying specific frequencies.

5. A diffuse sound field to immerse the listener in the sound.

29

3. Procedure

3.1 References and Observations

The first step in collecting resources was to inquire about past research in similar

projects. Because acoustic architecture is a well-established profession, finding reference

material was relatively easy. WPI’s Gordon Library had an excellent selection of

reference materials devoted to Sound, Acoustics, and Acoustic Architecture. The project

team’s efforts and findings in this area are well summarized in the Literature Review

section of this paper.

After discovering a sufficient amount of background information, the group

gained more information relative particularly to Spaulding Recital Hall, by questioning

faculty members of the WPI Music Division that conduct the musical ensembles in

question. Professor Weeks and Professor Falco supplied the team with their expert

judgments in identifying the problem with the hall. Professor Douglas G. Weeks,

Administrator of Applied Music, directs the Medwin String Ensemble, the Brass

Ensemble, and the Woodwind Ensemble. Director of Jazz Studies, Richard G. Falco

conducts the Jazz Ensemble.

To gain more hands-on insight into the sound of each group within the hall, the

IQP team generated a set of forms (see Appendix A) by observing the musical groups

during their rehearsals. The results of these findings helped the IQP team comprehend

the observation data collected from the directors through “first hand experience.” The

results of these observations can be seen in Appendix B.

30

3.2 MLSSA

With the aid of Professor Richard H. Campbell, an adjunct professor of the

Electrical and Computer Engineering department, the team used MLSSA (Maximum

Length Sequence System Analyzer) to calculate the acoustical characteristics of

Spaulding Recital Hall. MLSSA generated segments of pseudo-random pink noise

channeled through a dodecahedron loudspeaker array. This signal was used to excite the

room. The resulting impulse response was received by an omni-directional microphone.

The microphone’s output was connected to a sound level meter, which acted as a pre-amp

into the MLSSA card inside the computer. Additionally, the impulse response was

recorded through a pair of binaural microphones connected to a DAT (Digital Audio

Tape) machine. These microphones were mounted on a pair of eye glass frames, which

were worn by a team member. The team member was seated in a chair, beneath the

omni-directional microphone, to simulate an audience’s aural perception of the hall.

Multiple source and receiver positions were used to obtain various sets of data.

These data sets were attained to investigate the behaviors of distinct reflection patterns

resulting from the differences in source locations. Shown in figure 3.2.1 is a floor plan of

Spaulding Recital Hall, indicating each source and receiver location. Table 3.2.1 lists the

combination of source and receiver positions from which a MLSSA test was conducted.

31

32

Unoccupied Hall (Computer) Unoccupied Hall (Binaural) Occupied Hall (Binaural)

SPS1R1U.TIM SPS1R1L.TIM SPS2R1OL.TIM SPS1R2U.TIM SPS1R1R.TIM SPS2R1OR.TIM SPS2R1U.TIM SPS1R2L.TIM SPS2R2OL.TIM SPS2R2U.TIM SPS1R2R.TIM SPS2R2OR.TIM SPS2R3U.TIM SPS1R3L.TIM SPS5R4OL.TIM SPS3R1U.TIM SPS1R3R.TIM SPS5R4OR.TIM SPS3R2U.TIM SPS2R1L.TIM SPS5R5OL.TIM SPS3R3U.TIM SPS2R1R.TIM SPS5R5OR.TIM SPS4R1U.TIM SPS2R2L.TIM SPS4R2U.TIM SPS2R2R.TIM SPS4R3U.TIM SPS2R3L.TIM SPS5R4U.TIM SPS2R3R.TIM SPS5R5U.TIM SPS3R1L.TIM

SPS3R1R.TIM SPS3R2L.TIM SPS3R2R.TIM SPS3R3L.TIM SPS3R3R.TIM SPS4R1L.TIM SPS4R1R.TIM SPS4R2L.TIM SPS4R2R.TIM SPS4R3L.TIM SPS4R3R.TIM

Table 3.2.1: MLSSA Shot Filenames

33

Using the methodology outlined above, two sets of data were collected. The first

set of information was compiled in an unoccupied hall. Unoccupied, in this context,

refers to an area devoid of people and objects (i.e. chairs, pianos, percussive instruments,

etc.). The exception made in this case was the assumption that the risers in the hall were

permanent and would never be removed. A MLSSA “shot”, shown for source location

two and receiver location one is shown in figure 3.2.2.

Figure 3.2.2: An impulse response from MLSSA for source/receiver location S2R1. This plot represents sound pressure level (dB) versus time (ms).

This plot illustrates the impulse response of the unoccupied hall. The impulse response is

measured in volts and is plotted against time (milliseconds).

The second set of information was collected in an occupied hall. All the materials

and items normally present during a live performance were in the room. These items

included chairs, musical instruments, and most importantly, people. An audience and

performance ensemble were simulated, seated in the appropriate locations, to more

34

realistically represent the hall during a concert. The number of people present in the hall

during the testing was 62. A similar set of source/receiver locations, listed in table 3.2.1,

were used in obtaining the data. Once again, the information was gathered using the

computer and the DAT machine. As is normal practice, the team member wearing the

eye glasses was seated directly beneath the omni-directional microphone.

All of the raw acoustical information was stored in both the hard drive of the

computer, as *.TIM files, and the digital audio tape. A sufficient amount of data was

collected to begin the analysis of Spaulding Recital Hall. Since all of the analysis and

calculations needed to be done on a computer, the information stored on the DAT was

transferred to the computer by playing the recorded signal into the MLSSA software.

This process not only transferred the information from the DAT machine to the computer,

but it also saved it as a time file. Because of the DAT machine’s dual channel input, two

impulse response signals were stored for each MLSSA shot. This feature created two

time files and also allowed for an analysis procedure to be discussed later on.

35

The software package used to analyze the impulse responses of Spaulding Recital

Hall was MLSSA. With the MLSSA software, it was possible to compute all the

necessary acoustic parameters necessary for analysis. Each one of these calculations

could have been performed separately; however, the option to calculate them all at once

was chosen instead. A more in-depth description of MLSSA is contained in Appendix C.

The results of the rigorous computations were displayed in an organized tableau. An

example of an acoustical calculation tableau is shown in table 3.2.2.

IEC Octave Band Acoustical Parameters

Band Parameter

3 125

4 250

5 500

6 1000

7 2000

8 4000

9 8000

500- 4000

S [dB-SPL] 64.7 79.6 83.8 85.5 92.6 94.3 94.3 SPL- N [dB-SPL] -- -- 51.9 53.6 61.7 64.3 67.3 weighted SNR [dB] -- -- 31.9 31.9 30.9 30.0 27.0 Averages C50 [dB] 0.54 -1.49 -3.94 -2.29 -2.22 0.28 3.23 -1.615 C80 [dB] 5.46 3.21 1.92 0.93 1.65 3.58 6.7. 2.240 D50 [%] 53.1 41.5 28.8 37.1 37.5 51.6 7.8 39.640 TS [ms] 70.7 86.0 96.5 96.1 87.8 70.2 45.5 85.844 EDT-10dB [s] 0.866 1.130 1.188 1.215 1.083 1.017 0.662 1.105 RT-20dB [s] 1.423 1.254 1.420 1.287 1.192 1.045 0.920 1.212 (-5,-25) r -0.996 -0.993 -0.997 -0.999 -0.999 -1.000 -1.000 -0.999 RT-30dB [s] 1.422 1.431 1.280 1.264 1.179 1.020 0.681 1.189 (-5,-35) r -0.998 -0.994 -0.998 -0.999 -1.000 -0.999 -0.998 -0.999 RT-USER [s] 1.478 1.355 1.429 1.303 1.218 1.038 0.716 1.222 (-10,-25) r -0.995 0.986 -0.995 -0.998 -0.999 -1.000 -1.000 -0.999

Table 3.2.2: A sample calculation tableau from MLSSA for source/receiver location S2R1.

The acoustical information was gathered for every time file, saved as an ASCII file, and

imported into a Microsoft Excel spreadsheet.

Although all of the information displayed in the tableaus contained useful

information, only a few parameters were significant to this project’s research. The

properties of clarity (C80), early decay time (EDT), and reverberation time (RT-20) were

isolated from the rest of the data and placed in graphs for comparative analysis.

36

3.3 ODEON

A three dimensional computer-aided mathematical model of Spaulding Recital

Hall was created using the ODEON Room Acoustics software package. ODEON is an

acoustical analysis tool developed at the Technical University of Denmark and is unique

in that it is based on “ray-tracing” algorithms that were previously employed only in

visual rendering software packages. ODEON is covered in detail in Appendix D.

In order to create a mathematical model of the hall, a geometrical description of

Spaulding Recital Hall needed to be created. A surface file, containing a list of corners

and surfaces within the room, was produced using a simple text editor. The surface file

has been made available in Appendix E. The corners listed in this file defined each of the

significant corners in the room through the use of a three-dimensional coordinate system.

In order to make the production of this file easier, the symmetry of the room was

exploited. The origin of the coordinate system was placed in the middle of the two glass

doors, at the main entrance to the hall, on the floor. The x-direction was chosen as being

the length of the room, the y-direction corresponded to the width, and the z-direction

represented the height. A list of surfaces was then entered into the file, defined by the

corners creating it. These corners were listed as they appeared if one was to travel along

the edge of the surface in either direction. The last thing necessary in the surface file was

a definition of three sides of the room. The three sides defined in the surface file were the

floor (x-y), the west wall (x-z), and the south wall (y-z). Any three surfaces could have

been chosen as they are only used in graphical displays within the program.

The surface file was checked throughout its creation for any possible errors. The

final test performed on the room model was a “water-tightness” test. This process checks

37

to see if there are any leaks in the room where anything, specifically sound, might escape.

A room must be “water tight” before any calculations can be performed on it. The

finished three-dimensional view of the surface file is shown in figure 3.3.1.

Figure 3.3.1: Three-dimensional representation of the surface file.

In preparing the model for use, a number of things had to be added to it to make it

complete. Materials, each with their own set of absorption coefficients, were assigned to

each surface in the room. Most of the materials were chosen from the list of materials

provided with ODEON; however, one material was added to the list. The sound

absorbing panels, located around the main entrance of Spaulding Recital Hall, were

specially designed for the room. Therefore, the absorption coefficients of those panels

were obtained by the acoustic consulting firm of Tocci, Cavanaugh, and Associates and

entered into the material library file. The last things to be added to the model description

38

were the source and receiver locations. In order to make the theoretical calculations

match up as closely as possible to the real calculations, the source and receiver positions

for the MLSSA testing were used. The sources were chosen as omni-directional point

sources with the same sound pressure level output and placed in the same spot in three-

dimensional space. The receivers were placed in the same spot as the microphones and

all faced the sources accordingly.

Acoustical calculations were then performed on the room model. Identical

parameters such as clarity, early decay time, and reverberation time were found. Once a

set of numbers was calculated for each of the appropriate source/receiver locations, the

theoretical data was compared with the realistic data to see if a general curve was

followed. These curves of clarity, early decay time, and reverberation time, plotted as

sound pressure level or time versus frequency, needed to match rather closely. A nice

match indicates a useable mathematical model, whereas a bad match corresponds to an

unusable model. If a good match occurs, anything that is done to the theoretical model to

change any of the acoustical parameters should affect the real hall in the same manner.

This is the basis for using the theoretical model as a tool for analysis. Changes were

made to the model until a suitable curve fit was established.

3.4 Resonance Testing

As noted in the Literature Review, standing waves can produce a tremendously

annoying problem with a room’s sound. Through the mathematics provided in the

Literature Review, the individual resonant frequencies of the hall were calculated.

These frequencies were verified by conducting resonance tests in the room. A frequency

39

generator was directly connected to a mixing board and then to an amplifier positioned on

one side of the room. Using a microphone that was placed on the opposite side of the

room, also connected to the mixing board, allowed a comparison of the direct generator

signal and the collected signal. The results of this testing were then processed using a

computer algorithm. The methods employed by this program as well as the program’s

code are contained in Appendix F. A detailed description of the resonance testing

apparatus is contained in Appendix G.

3.5 Inter-Aural Cross Correlation

This final source of analytical data that was collected concerned the

“spaciousness” of the hall. A recently developed variable in room acoustics is IACC

(Inter-Aural Cross Correlation). This process involves taking the two binaural impulse

response signals and cross correlating them. Through extensive mathematical

manipulation, the spaciousness is calculated and then viewed as it pertains to the octave

bands between 250 and 4000 Hz.

The binaural impulse response signals of the occupied and unoccupied hall were

entered into a MathCAD worksheet (Appendix J). This MathCAD worksheet was

created by Professor Campbell to calculate the IACC of a hall. This computation was

executed twice, once for the unoccupied hall and once for the occupied hall. The same

source/receiver location of S2R1 was used each time. The information that this created

was contained in a table of values as well as a graph for visual analysis.

40

3.6 Tests of Hypotheses

Each group member carefully examined all of the collected information. A

meeting was then held with Professor Campbell to interpret all the data that was

collected. Potential reasons for the annoyance caused by performing in Spaulding Recital

Hall were discussed. It was then agreed upon, by all members of the group, to further

pursue these deficiencies and hypothesize about possible solutions. Prof. Campbell was

again contacted to aid the team with his expert opinions and experience. The hypotheses

were broken into two separate groups: minor changes and major changes. Minor changes

are modifications that can be easily accomplished in the room. The major changes

involve more permanent alterations, made possibly to the actual structure of the room.

A few of the minor changes were implemented with cylindrical absorbers

constructed by the IQP team. These absorbers were a moderately simple design based off

of the commercially available TubeTrap. The design, discussed in Appendix H,

incorporated a resonant cavity for absorption of a frequency range from 100Hz to 300Hz

in attempts to eliminate the modes of vibration in the room as well as an outer surface

that serves to diffuse high frequencies. Using locally available materials, the designs were

realized by the IQP team and put through a series of qualitative tests, noting the behavior

of the room for various positions of the absorbers.

Major changes took on a different life of their own. These alterations were not

meant to be implemented at all, merely as ideas for successive project teams to pursue

further in an attempt to permanently enhance the Spaulding Recital Hall’s sound quality.

The process of examining these solutions took place in two steps. The first step was to

calculate realistically achievable dimensions for physical apparatuses. The second step

41

involved simulating changes to the room using the model in ODEON. This was

performed by adding objects in the room and adjusting their absorption coefficients

appropriately (Appendix K). The acoustic calculations were performed again and the

outcome examined. Regardless of the results, this provided additional information and

guidelines for further projects to consider. Both sets of changes are discussed further in

section 5, Final Test Results.

42

4. Experimental Results

4.1 MLSSA Testing

The information contained in this section of the report summarizes the results of

the quantitative acoustical analyses. This includes, specifically, the data from MLSSA,

ODEON, the resonance testing and the interaural cross-correlation calculations.

Conclusions about the acoustical inadequacies of Spaulding Recital Hall were drawn

from this data and are discussed later in this report.

To aid in the discussion of this information, a reprint of the floor plan of

Spaulding Recital Hall appears below in figure 4.1.1.

43

44

The first source of empirical data to be discussed came from MLSSA. The

information gathered from this device laid the foundation for most of this project’s

findings. The three acoustical measurements relevant to this project were clarity (C80),

early decay time (EDT), and reverberation time (RT-20). The numerical data generated

by MLSSA was transferred to a spreadsheet in Microsoft Excel. Plots of the above

measurements, each versus frequency, were produced to allow an easier understanding

and comparison of the data.

Five sets of data that bore particular relevance to the IQP were chosen for study.

The sets provide for two group positions in both rehearsal and performance conditions.

They are as follows:

1. Binaural Comparison: Data taken from the unoccupied hall was gathered from both a binaural recording and a single omni-directional microphone. This data set is a comparison between these two data retrieval methods for the unoccupied hall.

1. S2 R1: Source on lower riser, reciever at moderate distance from entrance. This is a standard performance setup and is the configuration used to test the ODEON model of the recital hall.

1. Average of S2 with R1 and R2: Here the source is again on the riser, but the averaging of the two reciever locations (R1 with a direct path and R2 with a path through the column) lead to a better representation of the sound where an audience would be positioned..

1. Average of S5 with R4 and R5: Often, recitals utilize this corner as the performance space. This data set reflects this with the source positioned in the same corner and the average of two locations in the ‘audience’.

1. Average of S2 and S5, with R1, R2, R4 and R5: An average of the two previously mentioned group configurations with their respective reciever layouts. This set is representative of the overall acoustical conditions in Spaulding Recital Hall.

•Binaural Comparison

Due to constraints in the amount of time available to retrieve data from Spaulding

Recital Hall while it was occupied, the IQP team chose to use the binaural DAT recording

system to obtain the data. However, the majority of the data for the unoccupied hall was

45

collected previously with the omni-directional microphone, and an incomplete set with

the binaural DAT system. To establish the accuracy of the data taken, figures 4.1.2, 4.1.3

and 4.1.4 compare the binaurally recorded data to the direct omni-directional microphone

data.

C80 Binaural Comparison for Unoccupied HallSource 2, Reciever 1

-3

-1

1

3

5

7

9

11

13

15

125 250 500 1000 2000 4000 8000

Frequency [Hz]

C80 [dB]

Unoccupied C80 [dB]

Binaural C80 [dB]

Figure 4.1.2: Comparison of clarity for the binaurally recorded data and the computer recorded data.

46

EDT Binaural Comparison for Unoccupied HallSource 2, Reciever 1

0.3

0.5

0.7

0.9

1.

1.3

1.5

250 500 1000 2000 4000 8000

Frequency [Hz]

EDT [s]

Unoccupied EDT-10dB [s]

Binaural EDT-10dB [s]0.931

Figure 4.1.3: Comparison of EDT for the binaurally recorded data and the computer recorded data.

RT-20 Binaural Comparison for Unoccupied HallSource 2, Reciever 1

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000 8000

Frequency [Hz]

RT-20 [s]

Unoccupied RT-20dB [s]

Binaural RT-20dB [s]

Figure 4.1.4: Comparison of RT-20dB for the binaurally recorded data and the computer recorded data.

47

Figures 4.1.2, 4.1.3 and 4.1.4 are enumerated in table 4.1.1.

Octave Band Frequency (Hz) 125Hz 250Hz 500Hz 1000Hz 2000Hz 4000Hz 8000Hz C80 [dB] 1.22 0.9 1.87 -0.815 -0.435 1.01 0.91 EDT-10dB [s] -0.065 -0.17 -0.188 -0.0695 -0.0955 -0.052 -0.131 RT-20dB [s] -0.0705 -0.109 -2.2E-16 -0.004 -0.074 -0.098 -0.132

Table 4.1.1: Deviation of computer recorded data from binaurally recorded data.

Note that the results submitted in table 4.1.1 and figures 4.1.2, 4.1.3 and 4.1.4

have been determined to lie within the accuracy range dictated by the scope of this IQP.

Subsequent data points marked ‘unoccupied room’ have been obtained through the use of

the omni-directional microphone, and results marked ‘occupied room’ have been

obtained with the binaural DAT system.

48

•Average of S2 and S5, with R1, R2, R4 and R5

The following three plots in figures 4.1.5, 4.1.6 and 4.1.7 represent average values

that correspond to an overall sound in Spaulding Recital Hall. In figure 4.1.5, clarity is

presented for both the unoccupied and occupied room conditions. Recalling from the

Literature Review that desirable clarity ranges lie between the values of 0dB and 2dB, it

can be seen from figure 4.1.5 that the average clarity of Spaulding Recital Hall is less

than adequate both when occupied and unoccupied. Due to the fact that clarity is a

logarithmic ratio of the energy present in the last 80ms of the impulse response to the first

80ms, the negative values represent an area of pitches that suffer from lack of

articulation.

Clarity (C80)Average of Sources 2 and 5, with Recievers 1, 2, 4 and 5

-3

-1

1

3

5

7

9

1

13

15

125 250 500 1000 2000 4000 8000

Frequency [Hz]

C80 [dB]

Occupied C80 [dB]

Unoccupied C80 [dB]

Figure 4.1.5: Average clarity for all of Spaulding Recital Hall

49

Early decay time is measured in seconds and directly corresponds to the time

required for the impulse to decay by ten decibels. In the figure 4.1.6 that follows, a sharp

peak should be noted in the 500Hz octave band for both curves.

Early Decay Time (EDT)Average of Sources 2 and 5, with Recievers 1, 2, 4 and 5

0.3

0.5

0.7

0.9

1.1

1.3

1.5

125 250 500 1000 2000 4000 8000

Frequency [Hz]

EDT [s]

Occupied EDT-10dB [s]

Unoccupied EDT-10dB [s]

Figure 4.1.6: Average EDT for all of Spaulding Recital Hall.

50

Reverberation time (RT-20dB) is measured in seconds, and similar to EDT, it

represents the time required for the impulse to decay. However, RT-20dB is interesting

in that it is a measure of the time to decay 20dB extrapolated out to 60dB.

Reverberation Time (RT-20)Average of Sources 2 and 5, with Recievers 1, 2, 4 and 5

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000 8000

Frequency [Hz]

RT-20 [s]

Occupied RT-20dB [s]

Unoccupied RT-20dB [s]

Figure 4.1.7: Average RT-20dB for all of Spaulding Recital Hall.

51

•S2 R1

The following three figures (4.1.8, 4.1.9 and 4.1.10) are representative of the S2

R1 standard configuration.

Clarity (C80)Source 2, Reciever 1

-3

-1

1

3

5

7

9

11

13

15

125 250 500 1000 2000 4000 8000

Frequency [Hz]

C80 [dB]

Occupied C80 [dB]

Unoccupied C80 [dB]

Figure 4.1.8: Clarity for S2 R1.

Early Decay Time (EDT)Source 2, Reciever 1

0.3

0.5

0.7

0.9

1.

1.3

1.5

125 250 500 1000 2000 4000 8000

Frequency [Hz]

EDT [s]

Occupied EDT-10dB [s]

Unoccupied EDT-10dB [s]

Figure 4.1.9: EDT for S2 R1.

52

Reverberation Time (RT-20)Source 2, Reciever 1

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000 8000

Frequency [Hz]

RT-20 [s]

Occupied RT-20dB [s]

Unoccupied RT-20dB [s]

Figure 4.1.10: RT-20dB for S2 R1.

In figure 4.1.10 above, special notice should be made of the peak in the 500Hz

octave band, and how it is drastically minimized in the occupied room.

53

•Average of S2 with R1 and R2

The following three graphs in figures 4.1.11, 4.1.12 and 4.1.13 correspond to the

S2 performance configuration, with the averaged recievers in the ‘audience’.

Clarity (C80)Source 2, Average of Recievers 1 and 2

-3

-1

1

3

5

7

9

11

13

15

125 250 500 1000 2000 4000 8000

Frequency [Hz]

C80 [dB]

Occupied C80 [dB]

Unoccupied C80 [dB]

Figure 4.1.11: Clarity for the S2 R1 and R2 performance location on the risers.

54

Early Decay Time (EDT)Source 2, Average of Recievers 1 and 2

0.3

0.5

0.7

0.9

1.1

1.3

1.5

125 250 500 1000 2000 4000 8000

Frequency [Hz]

EDT [s]

Occupied EDT-10dB [s]

Unoccupied EDT-10dB [s]

Figure 4.1.12: EDT for the S2 R1 and R2 performance location on the risers.

Reverberation Time (RT-20)Source 2, Average of Recievers 1 and 2

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000 8000

Frequency [Hz]

RT-20 [s]

Occupied RT-20dB [s]

Unoccupied RT-20dB [s]

Figure 4.1.13: RT-20dB for the S2 R1 and R2 performance location on the risers.

55

•Average of S2 with R1 and R2

The next three figures (4.1.14, 4.1.15 and 4.1.16) represent data taken from the S5

performance configuration in the corner, with R4 and R5 averaged in the ‘audience’.

Clarity (C80)Source 5, Average of Recievers 4 and 5

-3

-1

1

3

5

7

9

1

13

15

125 250 500 1000 2000 4000 8000

Frequency [Hz]

C80 [dB]

Occupied C80 [dB]

Unoccupied C80 [dB]

Figure 4.1.14: Clarity for the S5 R4 and R5 performance location in the corner.

Early Decay Time (EDT)Source 5, Average of Recievers 4 and 5

0.3

0.5

0.7

0.9

1.

1.3

1.5

125 250 500 1000 2000 4000 8000

Frequency [Hz]

EDT [s]

Occupied EDT-10dB [s]

Unoccupied EDT-10dB [s]

Figure 4.1.15: EDT for the S5 R4 and R5 performance location in the corner.

56

Reverberation Time (RT-20)Source 5, Average of Recievers 4 and 5

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000 8000

Frequency [Hz]

RT-20 [s]

Occupied RT-20dB [s]

Unoccupied RT-20dB [s]

Figure 4.1.16: RT-20dB for the S5 R4 and R5 performance location in the corner.

57

4.2 ODEON Testing

The second source of acoustical information about Spaulding Recital Hall was

obtained from the model created in ODEON. The construction of this computer model

has already been described in the Procedure section of this report. The theoretical data

created by ODEON and the tangible data obtained by MLSSA were tabulated and

graphed to make comparisons of the two easier. Table 4.2.1 contains the data gathered by

MLSSA for the unoccupied Spaulding Recital Hall with the source/receiver location

S2R1. This data consists of early decay times, clarity values, and reverberation times.

Octave Band (Hz)

Early Decay Time EDT (s)

Clarity C80 (dB)

Reverberation Time, RT-20 (s)

125 0.866 5.46 1.423 250 1.130 3.21 1.254 500 1.188 1.92 1.420 1000 1.215 0.93 1.287 2000 1.083 1.65 1.192 4000 1.017 3.58 1.045

Table 4.2.1: Early decay time, clarity, and reverberation time results, generated by MLSSA, for source/receiver location S2R1 in the unoccupied Spaulding Recital Hall.

It is important to note that the data in table 4.2.1 is the same data used to create the plots

shown in figures 4.1.8, 4.1.9, and 4.1.10.

58

To test the validity of the ODEON model a set of data was generated

corresponding to the set shown in table 4.2.1. Identical parameters were chosen; S2R1

was the source/receiver location and the room was unoccupied. Table 4.2.2 shows the

values for early decay time, clarity, and reverberation time calculated by ODEON.

Octave Band (Hz)

Early Decay Time EDT (s)

Clarity C80 (dB)

Reverberation Time, RT-20 (s)

125 1.10 2.50 1.27 250 1.33 1.20 1.19 500 1.26 1.50 1.00 1000 1.24 1.60 1.13 2000 1.40 0.80 1.26 4000 1.15 2.00 1.35

Table 4.2.2: Early decay time, clarity, and reverberation time results, generated by ODEON, for source/receiver location S2R1 in the unoccupied Spaulding Recital Hall. This data was obtained with the original model of Spaulding Recital Hall.

59

A graphical comparison of tables 4.2.1 and 4.2.2 can be seen in figures 4.2.1,

4.2.2 and 4.2.3.

Clarity (C80) ODEON and MLSSA ComparisonSource 2, Reciever 1

-3

-1

1

3

5

7

9

11

13

15

125 250 500 1000 2000 4000

Frequency [Hz]

C80 [dB]

Unoccupied MLSSA C80 [dB]

Unoccupied Odeon C80 [dB]

Figure 4.2.1: Clarity for S2 R1 in the unoccupied Spaulding Recital Hall. A comparison of MLSSA and ODEON.

60

Early Decay Time (EDT) ODEON and MLSSA ComparisonSource 2, Reciever 1

0.3

0.5

0.7

0.9

1.

1.3

1.5

125 250 500 1000 2000 4000Frequency [Hz]

EDT [s]

Unoccupied MLSSA EDT-10dB [s]

Unoccupied Odeon EDT-10dB [s]

Figure 4.2.2: EDT for S2 R1 in the unoccupied Spaulding Recital Hall. A comparison of MLSSA and ODEON.

61

Reverberation Time (RT-20) ODEON and MLSSA ComparisonSource 2, Reciever 1

0.4

0.6

0.8

1

1.2

1.4

1.6

125 250 500 1000 2000 4000

Frequency [Hz]

RT-20 [s]

Unoccupied MLSSA RT-20dB [s]

Unoccupied Odeon RT-20dB [s]

Figure 4.2.3: RT-20dB for S2 R1 in the unoccupied Spaulding Recital Hall. A comparison of MLSSA and ODEON.

Little correlation can seem to be made between the ODEON model’s data and

MLSSA’s acquired data. Most prominently noticeable is the difference in reverberation

times. In figure 4.2.3 the plot of the MLSSA reverberation times compared to the

ODEON times shows a drastic difference greater than 0.4 seconds at the 500 Hz octave

band. Additionally, the trend that follows the 500 Hz band for ODEON indicates an

increase in RT-20dB with frequency, while MLSSA’s data points to the opposite.

Possible reasons for the inaccuracies of the ODEON model are discussed in

Appendix D. It is felt that these simplifications in the ODEON package may be

responsible for the disagreement in the clarity values. It is important to note that the most

relevant shortcoming of ODEON, concerning its use in this project, is that it does not

account for the existence of room resonances. As stated previously in the Literature

62

Review, the existence of room resonances is an important concern in smaller to mid-sized

rooms like Spaulding Recital Hall.

4.3 Resonance Testing Testing was conducted to quantitatively determine the existence of modes of

vibration in Spaulding Recital Hall. This test, hereafter referred to as resonance testing,

is described in Appendix G. In brief, the testing involved the measurement of the

resulting sound pressure level of a sinusoidal waveform after it was broadcast in

Spaulding Recital Hall at a known sound pressure level (SPL). The SPL of the tone at the

microphone was recorded as a function of its frequency, to give the ‘spectral view’ of the

hall shown in Figure 4.3.1.

-25

-20

-15

-10

-5

0

5

0 100 200 300 400 500 600 700 800 900 1000

Frequency{Hz]

Microphone level (dB)

Figure 4.3.1: Spaulding Recital Hall’s sound pressure level (SPL) response to the resonance testing described in Appendix G.

63

In figure 4.3.1, a higher point on the y-axis directly corresponds to a larger sound

pressure level. However, a positive y-axis value does not necessarily correspond to the

existence of a resonance. In fact, these sound pressure levels have some degree of

uncertainty associated with them due to the many variables present in this manner of

testing; the general shape of the curve must be examined.

A parametrically fit trend, represented by the heavier line, is provided to facilitate

an understanding of the data. This line indicates activity in the frequency ranges of 200

Hz to 300 Hz, 400 Hz to 500 Hz and 600 Hz to 700 Hz. These frequency ranges may

correspond to the problems concerning the early decay times in the 500 Hz octave band as

well as the clarity in the 250Hz band previously identified with the MLSSA and ODEON

packages. The existence of resonances within these frequency ranges may also account

for the discrepancies in ODEON and MLSSA for the clarity and reverberation times

encountered in section 4.2.

64

With the results of the resonance testing, it was necessary to re-visit the MLSSA

data to check the validity of the resonance test results. By producing three dimensional

plots of the MLSSA shot’s intensity (measured in dB) versus frequency (Hz) and time (s),

it was possible to determine if the hall exhibited any of the same behavior identified in

figure 4.3.1. Shown in figure 4.3.2 is a plot of the original noise signal taken from

source/receiver location S2R1.

Figure 4.3.2: Original MLSSA pink noise shot (dB) plotted versus time (ms) and frequency (Hz) taken from source/receiver location S2R1

From figure 4.3.2, it is possible to see the definite accentuation of the frequencies in the

vicinity of the 250 Hz and 500 Hz octave bands. Also, it is possible to note the existence

of an increase in sound pressure level in frequencies around 400 Hz from 150 ms to 230

ms.

4.4 Inter Aural Cross Correlation

65

An IACC (Inter Aural Cross Correlation) calculation measures the spaciousness

or “stereo effect” of a room. This process involves the comparison of two binaural audio

signals. The audio signals from a left and right microphone are compared against one

another and the relative similarity is measured. As with most acoustical measurements, a

number is generated for each of the octave bands. The result ranges from zero to one. An

outcome of one means that the two signals are identical, representing 100% similarity.

This occurs in an anechoic chamber, a room with no reverberation. In essence, there is no

perceiveable “stereo” sound. A result of zero means that the pair of signals are

completely different. This happens in a reverberation chamber. When this occurs, there

is too much “stereo” contained in the signals.

This type of acoustical measurement is relatively new in its creation. Its validity

in the world of acoustic architecture is the topic of many debates. While many

acousticians refuse to even think about IACC, there are many people that have made this

type of measurement in a number of auditoriums around the world. Typically, a large hall

exhibits IACC measurements around 0.3 or 0.4 in each of the octave bands starting from

250 Hz. A smaller room should have results slightly higher than these.

66

With the help of a MathCad worksheet, created by Professor Richard H.

Campbell, the IACC of Spaulding Recital Hall was calculated. Two sets of numbers

were generated; one for the unoccupied hall and one for the occupied hall. Both sets of

numbers were calculated using the binaural impulse responses from source/receiver

location S2R1. The results of these calculations are shown below in figures 4.4.1 and

4.4.2.

Figure 4.4.1: Results of interaural cross correlation calculations from MathCad for source/receiver locat