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SOUND: TRANSMISSION
When a sound wave impacts
upon the surface of a solid body,some portion of it's energy will
be reflected, some absorbed and
the rest transmitted through the
body. The relative proportion of
each depends on the nature of
the material impacted. This topic
concentrates on the transmitted
component.
Transmission Loss
If we consider the transmission
of sound through a partition, we
can actually measure the sound
energy on both the source side
(W sr c) and the receiving side
(W re c) to determine exactly
what fraction of the sound is
transmitted through. We can
thus determine the transmission
coefficient (t) for that partition
as follows:
t = Wr ec / Wsr c
The term Transmission Loss
(TL), or more commonly Sound
Reduction Index(SRI) are used
to describe the reduction in
sound level resulting fromtransmission through a material.
This is given by:
SRI = 10 l og ( Wsr c /Wr ec) = 10 l og ( 1/ t ) = - 10 l og ( t )
Composite Partitions
If a partition is composed ofmore than one element, for
example a wall with a door and a
window in it, then the effective
transmission coefficient must be
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found as an average of the area
weighted sum of each
component's transmission loss. If
the partition has n separate
elements, then the average
transmission is given by:
t Ave = S ( An t n) S An
Thus:
SRI Ave = - 10 l og( t Ave)
Frequency Dependence
Unfortunately, the SRI of nearly
all materials varies with
frequency. The main effect is the
mass law, with the effects of
resonance and coincidence also
contributing. Thus, SRI values
are normally shown as a curve
within a graph, as shown in
Figure 4 below. However, it is
possible to use a single SRI value
when dBA or dBB sound
weighting curves have beenapplied.
The Mass Law
Obviously, the greater the mass
of the wall, the greater the sound
energy required to set it in
motion. The mass law states that
every doubling of the mass of a
partition will result in a 6 dB
reduction in the level of sound
transmitted through it. It is given
by;
R = 20 l og (2p f m /roc) dB = 20 l og ( f m) - 47dB
Figure 1 - SRI curves for some example materials.
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where
f= the frequency (Hz),
m= the mass per unit area
(kg/m), and
roc= the characteristic
impedance of air (basically,
density times the speed ofsound: taken to be between
410 and 420 rayls for 20C
and 1 atm).
The mass law applies strictly to
limp, non-rigid partitions.
However, most materials used in
buildings possess some rigidity or
stiffness. This means that other
factors must really be
considered, and that the masslaw should only be taken as an
approximate guide to the amount
of attenuation obtainable.
Resonance and CoincidenceEffects
Sound attenuation in ordinary
building materials is the result of
an interplay between mass,
stiffness and damping. In
addition, the mass law is affectedby resonance at lower
frequencies and coincidence at
higher frequencies, as shown in
Figure 1 below.
Stiffness Controlled Region
At low frequencies (for most
building materials below 100Hz),
transmission depends mainly on
the stiffness of the wall, with
damping and mass having little
effect. The effectiveness ofstiffness in the attenuation of
sound transmission decreases by
6dB for every doubling of
frequency (one octave).
Figure 2 - Graph of resonance and coincidence effect.
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Resonant Frequencies
At slightly higher frequencies the
resonance of the wall begins to
control its transmission
behaviour. Because every panel
has a finite boundary and edge
fixings, it will have a series of
natural frequencies at which itwill vibrate more easily than
others. These are called resonant
frequencies and consist of a
fundamental frequency (having
the greatest effect), and integer
multiples of this fundamental
called harmonics (having less and
less effect). The fundamental
resonant frequency of a panel
can be calculated as follows:
Fr = 0. 45 * vL *b( ( 1/ l ) +( 1/ h) )
and:
vl = sqrt ( E / ( p * ( 1- s ) ) )
where:
b= the panel thickness (m),
l and h= length and height(m),
and
vl = the longitudinal velocity of
sound in the partition (m/s).
In the calculation of vl:
E = Young's modulus of
elasticity,s= it's Poisson ratio, and
p= density (kg/m).
To calculate harmonic
frequencies, simply replace the
number 1 in the first equation
with the required harmonic
number.
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Mass Controlled Region
At frequencies well above that of
the lowest resonant frequency,
the wall tends to behave as an
assembly of much smaller
masses and is then said to be
mass controlled. It is within this
range that the mass law directly
applies.
Critical Frequency andCoincidence
High frequencies cause bending
or ripple waves that travel
longitudinally along a wall or
panel. The wavelength of a
bending wave is different from
that of the incident sound wave
which created it except at one
frequency, the critical frequency.
Unlike compressional waves,
bending waves of different
frequencies travel at different
speeds. This means that for
every frequency above the
critical frequency, there will be
an angle of incidence at which
the wavelength of the bending
wave is equal to the wavelength
of the impacting sound. This
condition is known ascoincidence.
When coincidence occurs it gives
rise to a far more efficient
transfer of sound energy from
Figure 3 - Resonance occurs when a stiff panel flexes as a result ofincident sound waves.
Figure 4 - The coincidence effect when 'ripples' in a material arecreated by incident sound waves.
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one side of the panel to the
other, hence the big coincidence-
dip at the critical frequency. In
many thin materials (such as
glass and sheet-metal), the
coincidence frequency begins
somewhere between 1000 and
4000 Hz, which includes
important speech frequencies.
The lowest frequency at which
coincidence can occur is when
the angle of incidence of the
sound is at 90 (grazing
incidence) and can be calculated
from:
Fc = c / ( 1. 8 * h* v l * s i n ( a) )
where:
c = the speed of sound in air
(m/s),
h= the panel thickness (m),
vl = the longitudinal velocity of
sound in the partition (m/s), and
a= the angle of incidence.
Above the critical frequency,
panel stiffness begins to play the
most important role again.
Sound Transmission Class
To avoid the misleading nature of
an average SRI value and to
provide a reliable single-figure
rating for comparing partitions,
the sound transmission class
rating procedure has been widely
adopted. According to thisprocedure, the STC of a partition
is determined by comparing the
16-frequency SRI curve with a
standard reference contour. This
contour consists of 3 segments
with different vertical increments,
125-400Hz (15 dB), 400-1250Hz
(5 dB) and 1250-4000Hz (0 dB),
as shown in the Figure below.
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The calculation of this value,whilst not necessarily complex, is
quite laborious. It is found by
shifting this contour vertically
until some of the measured
values fall below the STC curve
and the following two conditions
are met:
1. The sum of all the
deficiencies do not exceed
32 dB.
2. The maximum deficiency
at any frequency does not
exceed 8 dB.
This shifting is always done in
integer steps and, when a
matching position is found, the
final STC rating is given by the
value of the reference curve at
500 Hz. The SoundTool is a
software program which calculate
this value much faster and easier
than hand calculations.
Altering the TransmissionLoss of a Panel
Resonance and coincidence
effects cannot be eliminated. If
the designer aims to create the
maximum SRI, an attempt shouldbe made to get resonant
frequencies as low as possible
(preferably well below the
audible range) and the critical
frequency as high as possible
(preferably well above the
audible range). Whilst it is not
possible to apply a generic
solution to all panels, the
following general relationships dohold:
Reducing the stiffness of a
panel lowers it's resonant
Figure 5 - Sound Transmission Class (STC) curves.
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frequency and raises it's
critical frequency, basically
increasing the region for
which the mass law
applies.
Increasing panel mass also
lowers resonant
frequencies and raises the
critical frequency.
Decreasing panel thickness
raises the critical
frequency but generally
reduces panel mass.
Increasing the amount of
damping applied to the
panel will not alter the
frequencies of resonance
and coincidence but willact to reduce their effect.
Good insulation is therefore a
combination of low stiffness, high
mass and high damping (given
cost constraints).
NOTE: The most common
method of adding damping is to
apply a thick layer of mastic-like
material to one side of the panel.This type of treatment is only
effective on materials that have
low mass and an inherent lack of
damping. It would be useless on
thick concrete walls, for example,
but very effective on metal
automobile panels.
Multi-Layer Partitions
As just discussed, the insulationof a single-leaf panel can be
improved in a number of ways,
but this process can only
continue up to a certain point
given the exponential increase in
mass required. Consider the
example of a single brick wall
with an SRI of 22dB. To increase
this to an overall 40dB in all
regions, the mass must be
increased to 8 times the original
(2^3). This is clearly impractical
from a building perspective.
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Consider, on the other hand, the
fact that the wall already has a
22dB SRI. If we were to build
another brick wall right next to
it, we could (in theory) achieve a
further drop of 22dB. A situation
approaching this is possible if the
two walls were completely
separated from each other withno common links, footings or
edge supports, and an air gap
greater than a metre between
them.
Unfortunately, this is often just
as impractical as vastly
increasing the mass of the wall.
In practice, walls do have
common supports at the edges.
It is also rare to find a cavity wallwith more than few centimetres
of air gap.
On the other hand, it is possible
to create composite or sandwich
panels whose total SRI does
approach that of a double wall, if
the following points are
considered:
Well sealed cavities canresult in an increase in
sound insulation well
above mass law (6-8dB),
assuming the cavity is at
least 100mm deep.
Use of layers of different
thickness can greatly
assists in mismatching
resonant and critical
frequencies across thepanel.
The use of absorbent
materials within the
cavities can help to further
reduce transmission.
Only resilient elastic
materials should be used
as wall ties and suspension
members to reduce anydirect connection between
layers.
If required, only widely
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spaced and staggered
studs should be used
within partitions.
Caulking and sealants
should be used to
eliminate perimeter sound
leaks.
NOTE: The very last point isquite important as it alludes to
flanking. The highest achievable
SRI value for a partition is about
55-60dB.
Above 45-50dB, flanking paths
become more and more
important. This explains why
multiple-layer (three or more)
partitions do not offer any
significant improvement over
double-leaf construction.
The following are some examples
of different building sections and
their corresponding transmission
loss values. It is worth spending
some time looking at these
details as it will give you some
idea as to the requirements to
meet different values.
Partitions and Panels
Masonry Wall Sections
Floors and Ceilings
Flanking
There are often several other
paths sound can follow apart
from the direct path through the
panel. These include air
conditioning ducts, through
ceiling spaces, around edge
fixings, etc. As the designer, you
must always be thinking about
possible flanking paths whenever
you are doing acoustically
sensitive details.
This applies to air seals as well -
it is often better to have a tight-fitting lightweight door than a
loose-fitting heavy one.
http://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Panelshttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Masonryhttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Floorshttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Floorshttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Masonryhttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Examples#Panels8/14/2019 _ Sound_ Transmission _ Archived Ecotect WIKI.pdf
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previous next up
Sound:Propagation
SoundTransmission:
Examples
For Those Interested
Some clarifying points [From
Norton, M.P., Fundamentals of
Noise and Vibrational Analysis for
Engineers. Section 3.9].
1. If Wnis the natural
frequency of a panel and
Wis the frequency of
excitation:
when W> Wn
mass dominates.
2. If a panel is mechanically
excited, most of the
energy is produced by
resonant panel modes
irrespective of W.
3. If a panel is acoustically
excited by incidence, its
vibrational response
comprises both a forced
vibrational response at W
and a resonant response
at all relevant natural
frequencies which are
excited by the interaction
of the forced bending
waves with the panel
boundaries.
Related Links
Transmission Loss Explained
http://www.domesticsoundproofing.co.uk/tloss.htm
Examples
Figure 6 - Two different partition details illustrating the effects offlanking.
http://wiki.naturalfrequency.com/wiki/Sound_Propagationhttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Exampleshttp://wiki.naturalfrequency.com/wiki/Soundhttp://www.domesticsoundproofing.co.uk/tloss.htmhttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Exampleshttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Exampleshttp://www.domesticsoundproofing.co.uk/tloss.htmhttp://wiki.naturalfrequency.com/wiki/Soundhttp://wiki.naturalfrequency.com/wiki/Sound_Transmission_Exampleshttp://wiki.naturalfrequency.com/wiki/Sound_Propagation8/14/2019 _ Sound_ Transmission _ Archived Ecotect WIKI.pdf
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