The Physics of Music:
Environmental Acoustics
James Bernhard
In the first part of the semester, we discussed the fact that sound
waves go through three stages:
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Production
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Transmission
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Reception
At the start of the semester, we worked digitally, which allowed us
to focus on reception
We then shifted our focus to sound production
We now turn our attention to transmission. . .
When a sound is emitted unobstructed, it emanates in all directions
In open air, sound intensity level drops off by about 6 dB when the
distance from the source is doubled
Human beings have an excellent ability to localize sounds, or
determine their source
For sounds of low frequency, we observe a slight difference in the
time of arrival (or the phase, for steady sounds) at our two ears
For sounds of higher frequency (above about 1000 Hz), we
perceive a difference in the sound level in our two ears because of
the sonic shadow of our head
This sonic shadow isn’t as pronounced for low frequency sounds
because (having a longer wavelength) they diffract around the
head more strongly
Human beings generally find it easier to localize high-pitched
sounds than low-pitched sounds
If the sound is indoors, it will reflect off the walls, ceiling, and floor
to some degree
Some terms we use to classify sound waves that reach a listener
are:
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direct sound consists of sound waves that propagate from
source to listener without being reflected
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reverberant sound or reverberations consists of sound waves
that reach the listener after being reflected
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early sound refers to the first group of reflected sound waves,
which reach the listener within about 50-80 ms of the direct
sound
Early sound waves tend to arrive individually, while reverberant
sound waves are all clustered together, as pictured at the
AV Info website
Direct sound is much easier to localize and analyze, but the arrival
of reflected sound complicates perception
Early reflections will have essentially the same spectrum and time
envelope as the direct sound, and if they arrive within about 50-80
ms of the direct sound, we do not perceive them as separate sounds
Instead they reinforce the direct sound
The perceptual limit is about 50 ms for rapidly changing sounds
such as speech, but is close to 80 ms for slowly varying music
When we localize a sound that is reinforced by reflected sound, we
base our localization on the first sound to arrive (which is
ordinarily the direct sound) if
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successive sounds arrive within about 35 ms
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the successive sounds have spectra and time envelopes
reasonably similar to the first sound
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the successive sounds are not too much louder than the first
sound
This is called the precedence effect (or the Haas effect)
In a study of the world’s leading concert and opera halls, Beranek
(1996) found that concert halls are described as “intimate” when
the delay time between the direct and first reflected sound is less
than 20 ms
In a traditional rectangular-shaped auditorium, the first reflection
for most listeners comes from the nearest side wall, although those
near the center may get it from the ceiling
In larger halls, some listeners may be far enough from the walls and
the ceiling that they don’t receive the first reflected sound in this
time interval
To help alleviate this, reflecting surfaces of some type are often
suspended from the ceiling
However, recent studies have shown that early reflections from
ceilings, ceiling reflectors, and side walls are not perceptually
equivalent in judging “intimacy” of a hall
One study showed a high preference among listeners for concert
halls with ceilings sufficiently high that the first reflected sound
comes from a side wall
Other studies have found that if the total energy from side wall
reflections is greater than the energy from overhead reflections,
then the hall has a desirable “spatial responsiveness” or “spatial
impression”
The behavior of reverberant sound is far too complicated to be
described by a single number
However, if you had to choose a single number to describe it, the
reverberation time at midfrequency (500 to 2000 Hz or so) gives a
fair indication of the “liveliness” of a hall
The reverberation time of a sound is the time for it to decrease by
60 dB; look at the decibel level chart in wikipedia to see what this
corresponds to
Reverberant sound, like the early sound, reinforces the direct sound
and adds to the overall loudness (which can be important in a
large auditorium), but too great a level of reverberant sound can
result in a loss of clarity
Direct sound should be substantially louder than reverberant sound
at all locations in a hall, which sometimes calls for electronic
reinforcement of direct sound
For a full-size symphony orchestra, most listeners find the direct
sound level to be optimal when they are seated about 20 m (60 ft)
In a bare room where all surfaces absorb the same fraction of the
sound that reaches them, the reverberation time is proportional to
the room volume divided by the room’s surface area
In this idealized model, larger rooms have longer reverberation
times (as is generally true)
However, if some surfaces absorb a higher fraction of sound, then
that will decrease the reverberation time; also, air itself absorbs
sound too
With these complications, a more accurate formula for
reverberation time in a large concert hall is:
reverberation time = 0.161
V
,
A + kV
where V is volume, A is the “total absorbtion” coefficient of the
hall, and k depends on the temperature and humidity
Some criteria for good acoustics:
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Adequate loudness
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Uniformity
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Clarity
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Reverberance, or liveliness
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Freedom from echoes
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Low level of background noise
Note that reverberance varies with frequency; it is often desirable
to try to obtain reverberance specifcally for low frequencies, as the
hyperphysics website describes
The scientific principles behind acoustic design of concert halls are
well studied and fairly well understood
In spite of this, some concert halls (both old and new) have
acoustical problems
The most common problem leading to these is poor
communication among architects, acoustical designers, building
contractors, and musicians who use the hall
Music and acoustics developed largely separately, so they often
have different vocabularies
In his 1996 book on concert halls, Beranek attempts to bridge the
language gap by defining some terms in a way that both musicians
and acousticians can understand them, such as:
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intimacy or presence: music played in the hall gives the
impression of being played in a small hall.
reverberation: sound that persists in the room after the tone
has stopped. Liveliness refers to reverberation for tones above
about 350 Hz.
spaciousness in the sense of auditory source width (ASW): the
sound appears to emanate from a source wider than the visual
width of the source.
spaciousness in the sense of listener envelopment (LEV): the
reverberant sound appears to come from all directions
clarity: the degree to which discrete sounds in a musical
performance stand apart from each other.
warmth: the liveliness of the bass, or the fullness of the bass
tones (about 75-350 Hz) relative to the midfrequency tones
(350-1400 Hz). Dark also refers to a strong bass.
Each concert hall is better suited to some types of music more
than others
For example, the Royal Festival Hall in London is considered “dry”
(with a 1.5 s reverberation time), which can be a good
environment for chamber music and Baroque music
This has recently be modified electronically with some “assisted
resonance”
The Royal Albert Hall in London has a long reverberation time
(about 2.6 s, or up to 3.4 s for low frequency sounds) and so works
better for music such as Tchaikovsky’s 1812 Overture
In addition to the general criteria for good acoustics, concert halls
have other desirable aspects, such as:
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spaciousness, in both the senses of auditory source width and
listener envelopment
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slow initial rate of decay, which turns out to be more
important than the total reverberation time in assessing the
desirability of the hall
Some things to avoid in concert hall design:
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echoes (sounds not appearing until after about 50 ms), which
are usually due to the rear wall
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flutter echoes (a series of echoes in rapid succession), which
are often due to reflections between two highly reflective
parallel surfaces
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sound focusing, which can be caused by reflection from a large
concave surface
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sound shadows, which can occur under balconies at the rear of
a hall
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background noise
For more on sound focusing, let’s look at the
hyperphysics website
A study of 22 European concert halls by Schroeder, Gottlob, and
Siebrasse (1974) found:
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The greater the early decay time, the more desirable the hall,
up to a reverberation time (determined from the early decay
time) of 2 s; above 2 s, the opposite
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narrow halls were generally preferred to wide ones
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listeners showed considerable preference for a high binaural
dissimilarity, as might result from a high degree of asymmetric
sound diffusion
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halls with less definition were preferred, where definition refers
to the ratio of energy in the first 50 ms to the total energy of
the sound
Many halls considered to have good acoustics have a “shoebox”
design, which has given rise to many more halls of this shape
Avery Fisher Hall in New York City (originally called Philharmonic
Hall and housed in the Lincoln Center for Performing Arts) makes
an interesting case study in acoustical design
It opened in 1962 and underwent many renovations between 1962
and 1976, when it was completely rebuilt
It was designed by architect Max Abromovitz after an extensive
research study by acoustician Leo Beranek of the world’s leading
concert halls
Acoustical expertise was provided by Beranek’s firm
The 1962 opening was to be spectacular, but most musicians and
listeners were disappointed by some major defects:
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weak bass
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lack of liveliness
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echoes from the rear wall
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inadequate sound diffusion
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poor hearing conditions for the music on stage
Scientists from Bell Telephone Laboratories were called on to
evaluate the acoustics, and a distinguished committee of acoustical
consultants were called on to recommend improvements
Changes made during the summers of 1963, 1964, 1965, 1969, and
1962 cost more than $2 million and improved the hall some
In 1975, the hall was completely redesigned more along the lines of
Boston’s Symphony Hall and the more recent Kennedy Center in
Washington and Orchestra Hall in Minneapolis, costing more than
$5 million
So what went wrong?
Beranek maintains that the final plans were expanded and modified
without his consent or that of the orchestra
Seating capicity was enlarged from 2400 to 2600, and the side
walls were spread out to give a more “modern” fan shape
The adjustable ceiling was eliminated for financial reasons, as were
some irregularities on the side walls that were to serve as sound
diffusers
136 panels (“clouds”) were suspended from the ceiling to provide
early reflections, but later research indicated that ceiling reflections
are not as desirable as wall reflections for listeners’ assessment of
the hall
Also, the designers had planned to try to optimize some acoustical
parameters during a “tuning week” after the hall was built
Overall, the hall had insufficient diffusion of sound, which resulted
in a decay curve having a different rate at the start and toward the
end
The total reverberation time was fine, but the initial decay was too
rapid, which gave the impression of dryness
Buildings besides concert halls have some other considerations
Churches and synagogues are supposed to accomodate both
speech and music, which leads to a difficulty in trying to settle on
a good reverberation time
Historically, most of the cathedrals and churches in Europe have
long reverberation times, giving emphasis to music over speech
Nowadays, background noise, such as from HVAC systems, is an
important consideration
Classrooms also have such considerations: reverberation, HVAC
background noise, and noise from outside the classroom