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ound: Transmission | Archived Ecotect WIKI

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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.
http://wiki.naturalfrequency.com/wiki/SoundToolhttp://wiki.naturalfrequency.com/wiki/SoundTool


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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#Panels


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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_Propagation


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