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THE ACOUSTICS OF ROOMS
Josiah Killam
PHYS 193: The Physics of Music
Prof. Steven Errede
University of Illinois at Urbana-Champaign
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For my project for The Physics of Music, I decided to research the acoustic properties of
different rooms, and how rooms for specific acoustically purposes are built. These rooms include
special auditoriums, whispering galleries, reverberation rooms, and anechoic chambers.
These rooms are built by acoustical engineers, or acousticians, who are scientists in the
field of acoustics. Acoustics, derived from the Greek word “ακουστικός (akoustikos)” meaning
“of/for hearing”, is described as the science of all mechanical waves through a solid, liquid, or
gas. These mechanical waves include vibration waves, sound waves, ultrasound waves, and
infrasound waves. The specific branch of acoustics that are used in the design of auditoriums and
the like are sound waves.
So how do sound waves react in an environment like an auditorium? The intensity of
sound obeys a law of physics called the inverse square law. The ISL states that the intensity of a
sound is equal to the source power divided by the area of the sphere of which the point of
measurement lies on the surface of, and the source is the center of (see diagram below for visual
representation and equation).
This is the problem acoustical engineers must face when designing an auditorium: how can you
prevent the sound depreciation caused by the inverse square law? Luckily for the engineers, there
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are other things that have an effect on sound waves besides the inverse square law. Three majors
factors acoustical engineers use to design rooms are reflection, absorption, and reverberation.
Reflection is when sound hits a solid object and “bounces” off of it in a different
direction. It is the cause of such things like echoes, and is the reason why devices like sonar are
possible. The science behind reflection is another law, called the law of reflection. This law does
not only apply to sound waves, but to many other things ranging from light to the way a billiard
ball bounces off of the side of the table. The law of reflection states that the angle made by the
incident wave and the surface is equal to the angle made
by the reflected wave and surface (shown in the figure to
the left). The problem with reflection is that the reflected
waves can interfere with incident waves and mess with the
sound of the performance, constructively or destructively. The challenge of architectural
engineers is to create a space so the waves reflected off of the walls of the auditorium
constructively disturb the incident waves, producing a louder sound intensity.
But when a sound wave hits the wall of an auditorium, not all of the sound is reflected.
Another key factor in acoustical management is absorption. Absorption is the second part of a
wave hitting a wall. Instead of “bouncing” back, some of the sound is “absorbed” through the
material, causing the reflected wave to have less intensity than the incident wave. In fact, the
intensity of the incident wave is equal to the intensity of the reflected wave plus the intensity of
the absorbed wave. Depending on the purpose of the room being designed, acoustical engineers
may want to maximize or minimize absorption. Anechoic chambers are an example of the
former, while basic auditoriums are an example of the latter, both of which I will discuss in more
detail further on. How well a room absorbs sound is quantified by the effective absorption area of
the walls, which is calculated using the dimensions of the walls and the absorption coefficient,
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which is a constant that differs between materials and is equal to the absorbed wave divided by
the incident wave.
The third, and most important for auditorium purposes, effect on sound waves is
reverberation. Reverberation is caused by the collection of reflected waves in an enclosure, and
is used to overcome the inverse square law problem that acoustical engineers are faced with. Too
much reverberation, however, can cause sound waves to sound muddy and unarticulated, which
is never good for an auditorium setting. To perfect the level of reverberation, a quantity of
“reverberation time” is used. Over
time, the sound waves reflecting off
of surfaces will steadily decrease
because of the previously-discussed
property of absorption, thus the
intensity of the sound will slowly
diminish. The reverberation time is calculated by the time it takes for a sound’s intensity to
decrease by 60deciebels, or 60dB, below its original intensity. The formula for a reverberation
time is R = .161V/S, where R is reverberation time, V is the volume of the room in meters3, and
S is the total effective absorbing area of all walls, or the absorption constant multiplied by the
area of each wall.
So what structures to acoustical engineers work with, and how do they calculate what a
room should look like? Well there are plenty of different types of rooms they create, each with
its own purpose, and thus its own levels of absorption and reflection to create a perfect
reverberation. These rooms include auditoriums and lecture halls, anechoic chambers,
whispering galleries, and reverberation rooms.
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When an acoustical engineer works on the design for an auditorium or a lecture, there are
a lot of things they must take in to account. Firstly, they need effective projection of the sound all
the way to the rear end of the room. In other words, they must overcome the inverse square law.
That is conquered using a high ceiling of a reflective material and a specifically long
reverberation time. In general-use auditoriums, where music needs a bit of reverberation and
resonance through the halls, the prime reverberation time is 1.5-2.5 seconds. In auditoriums for
music-only use, the wanted reverberation time is greater, while in auditoriums for speaking
purposes, such as lecture halls, the desired reverberation time is lower. Another thing acoustical
engineers must worry about is blocking the direct path of sound. Clarity of sound can be
diminished by anything in the way of the direct sound wave from the source to the listener. Even
dispersion of a sound is also very important, else there may be prominent, unwanted echoes, or
reverberation “dead spots”, meaning very low reverberation time. The way to create an even
dispersion of sound is to avoid large, flat surfaces for sound to reflect off of. Instead, acoustical
engineers create halls that have angled, broken segments of wall on either side, and have the
walls slowly get closer as you go more towards the rear of the auditorium, as opposed to laying
them parallel.
The first building that was created with the use of acoustics in mind was the Symphony
Hall in Boston, Massachusetts. Created in 1900, it was designated a US National Historic
Landmark in 1999 and is still today among the top three concert halls in the world for its
acoustics. The designer, Clement Sabine, was an assistant professor of physics at Harvard
University, who ended up creating the formula for reverberation time, which is known at the
Sabine Formula, or, as previously mentioned, R = .161V/S.
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Anechoic chambers are exactly what they sound like: rooms that are created for the
purpose of minimizing echoes, thus reflection, as much as possible. They focus on creating
surfaces that will complete absorb any sound wave hitting them, creating a perfect, soundless
room for many different sorts of tests that would be otherwise disturbed by the noises of the
normal world. There are two ways of making an anechoic chamber: tiles, and pyramidal. The
former consists of flat plates of ferrite fixed to all interior surfaces of the room. It is the more
durable of the two, but is less effective at higher frequencies. The second way of making an
anechoic chamber, pyramidal, consists of rubbery foam in the shape of pyramids jutting out of
the wall from all areas. The length of these pyramids depends on the frequency desired for
testing. The length of the pyramids is roughly one-fourth of the wavelength, which is equal to the
velocity of the wave divided by
its frequency. Pyramids in an
anechoic chamber vary from 2
inches to 24 inches in length.
TILES
PYRAMIDAL
A whispering gallery is an interesting piece of acoustic architecture. It is usually a
circular or elliptical area enclosed beneath a dome. The interesting portion of this is that if one
stands at a certain area of the gallery and whispers, someone in a completely different part of the
room can hear the whisper like it originated right next to them. This is because the sound is
carried by a specific type of wave called a whispering-gallery wave, which travel around
concave surfaces. The sound from one end of the chamber travels around the circumference of
the circle to the point directly opposite from it, so that nobody except a person standing in the
second spot can hear what the person whispered. These waves were originally discovered in the
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whispering gallery of St Paul’s Cathedral by Lord Rayleigh, an English physicist who discovered
argon.
Opposite of anechoic chambers, reverberation rooms are designed for the purpose of
complete reflection and zero absorption. To create this effect, reverberation rooms are large
chambers with very hard exposed surfaces. These surfaces are also all non-parallel to help to
create standing waves, which are waves that remain in a constant position, thus not diminishing
over time. Much like the anechoic chambers, these rooms are used for experiments, but different
experiments than the anechoic chambers. A specific type of reverberation room used for music
recording is called an echo chamber.
Through my research, I have discovered the purpose of acoustics in architecture, and I’ve
learned why each part of an auditorium is created just like it is, for each part is where it is for a
specific reason. I also learned much more about absorption, reflection, and reverberation, and all
of the mathematic properties behind each one of them. I now know much more about both
architecture and acoustics, and the physics and mathematics behind both of them.
Works Cited
Backus, John. The Acoustical Foundations of Music. New York: Norton, 1977. Print.
“Reverberation” N.p, n.d. Web. 4 Dec 2013
http://hyperphysics.phy-astr.gsu.edu/hbase/acoustic/reverb.html
“What is Acoustics?” N.p, n.d Web. 29 Nov 2013
< http://www.physics.byu.edu/research/acoustics/what_is_acoustics.aspx>
“The Quietest Room In The World” N.p, Patricia Kelly 1 Nov 2013
< http://tcbmag.com/Industries/Technology/The-Quietest-Room-in-the-WorldSeptember-2008>