Sound insulation Sound insulation

(1)

23 November 2012 Sound insulation 1

Sound insulation

(2)

16 November 2012 Sound Absorption 2

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 r + a + t = 1

(3)

16 November 2012 Sound Absorption 3

Materials: sound insulating & sound absorbing Materials: sound insulating & sound absorbing

Sound absorbing materials must not be confused with sound insulating materials:

Sound Insulating material:

Heavy and stiff, minimizes the transmitted power “W_t”.

Sound Absorbing material:

Soft and porous, minimizes the reflected power “W_r”.

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The Sound Reduction Index R The Sound Reduction Index R

With regard to a sound imping over a wall we define t as:

• transmission coefficient:

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)

Wo t  Wt

 

 

 t

R 1

log

10

₁₀

(5)

Change of R with frequency Change of R with frequency

4 different frequency ranges can be identified:

• Rigidity region, R drops by 6 dB/octave.

• Resonance region (the whole panel is affected by resonances and antiresonances).

• Mass region, R increses by 6 dB/octave.

• Coincidence region (coincidence between wavelength in air and inside the flexural vibrations of the panel make the Sound Reduction Index to drop).

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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

Double Wall R = 36 dB Single Wall

R = 30 dB

Two separate walls R = 60 dB

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Coincidence frequency

• Example: steel, F

cr

=97700 Hzm

²

/kg, s’ = 8.1 kg/(m

²

mm)

• s = 10mm, hence s = s ’ s = 8.110 = 81 kg/m

²

• f

coinc

= F

cr

/s= 97700/81 = 1206 Hz

(8)

Sound Insulation D vs Sound Reduction Index R

• The Sound Reduction Index R is defined by:

• The Sound Insulation D is defined by:

• We can make an energy balance of the

energy passing through the separating wall, having surface S_div, and reverberating in room 2, having an equivalent absorption area A₂:

• After some math passages, we get the relationship between R and D:

R 10× log 1 t

I

₁

× S×t  I

₂

× A

₂

R L

₁

- L

₂

+10× log S

_div

A

₂

R D+10× log S

_div

A

₂

D  L

₁

- L

₂

(9)

Apparent Sound Reduction Index R’

• Theory – definition of t and R

• Practice – lab measurement (R) no flanking transmission

• Practice – in situ measurement (R’) significant flanking transmission

R³ R' ( R- R' ) ^{@ 3¸5} ^dB

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Weighted Sound Reduction Index R

_W

• 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.

Sound insulation Sound insulation