# Sound insulation

```Sound insulation
23 November 2012
Sound insulation
1
Sound against a wall
• Balance of sound energy
impinging over a wall
• The energy balance shows
three main fluxes:
– Reflected
– Absorbed
– Transmitted
• Hence three coefficients are
defined, as the ratios with the
impinging energy
23 November 2012
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Sound
SoundAbsorption
insulation
r+a+t =1
2
Materials: sound insulating & sound absorbing
Sound absorbing materials must not be confused with sound insulating
materials:
Sound Insulating material:
Heavy and stiff, minimizes
transmitted power “Wt”.
the
Sound Absorbing material:
Soft and porous, minimizes
reflected power “Wr”.
23 November 2012
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the
Sound
SoundAbsorption
insulation
3
The Sound Reduction Index R
With regard to a sound imping over a wall we define t as:
• transmission coefficient:
Wt
t
Wo
It is the ratio between the transmitted power Wt and the incident
power Wo.
The Sound Reduction Index R of a wall characterized by a
transmission coefficient t is given by:
• Sound Reduction Index:
(dB)
23 November 2012
Sound insulation
1 
R  10log10  
t 
4
Change of R with frequency
4 different frequency ranges can be identified:
• Rigidity region,
6 dB/octave.
R
drops
by
• Resonance region (the whole panel
is affected by resonances and
antiresonances).
• Mass region,
6 dB/octave.
R
increses
by
• Coincidence region (coincidence between wavelength in air and inside the
flexural vibrations of the panel make the Sound Reduction Index to drop).
23 November 2012
Sound insulation
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The mass law
R = 20 × lg (s × f ) - 42.5
(theoretical)
R = 20 × lg (s × f ) - 44.0
(practical)
• The value of R increses by 6 dB when doubling the frequency.
• The value of R increases by 6 dB when doubling the mass of the wall
Single Wall
Double Wall
Two separate walls
R = 30 dB
R = 36 dB
R = 60 dB
23 November 2012
Sound insulation
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Coincidence frequency
• Example: steel, Fcr=97700 Hzm2/kg,  = 8.1 kg/(m2mm)
• s = 10mm, hence  = s = 8.110 = 81 kg/m2
• fcoinc = Fcr/ = 97700/81 = 1206 Hz
23 November 2012
Sound insulation
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Sound Insulation D vs Sound Reduction Index R
•
•
The Sound Reduction Index R is defined by:
1
R = 10× log
t
The Sound Insulation D is defined by:
D = L1 - L2
•
We can make an energy balance of the energy
passing through the separating wall, having
surface Sdiv, and reverberating in room 2,
having an equivalent absorption area A2:
I1 × S × t = I 2 × A2
•
After some math passages, we get the
relationship between R and D:
23 November 2012
Sound insulation
Sdiv
R = L1 - L2 +10 × log
A2
Sdiv
R = D +10 × log
A2
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Apparent Sound Reduction Index R’
• Theory – definition of t and R
• Practice – lab measurement (R)
no flanking transmission
R ³ R'
( R - R') @ 3¸ 5
dB
• Practice – in situ measurement (R’)
significant flanking transmission
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Sound insulation
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Weighted Sound Reduction Index RW
• A reference curve is shifted down at 1 dB steps, until the sum of
unfavourable deviations becomes smaller than 32 dB
• At this point, the weighted value of the Sound Insulation Index, Rw,
is read on the reference curve at the frequency of 500 Hz.
23 November 2012
Sound insulation
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