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Sound insulationSound insulation

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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

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Materials: sound insulating & sound absorbingMaterials: 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 “Wt”.

Sound Absorbing material:

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

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The Sound Reduction Index RThe Sound Reduction Index RWith 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)

WoWtt

t

R 1log10 10

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Change of R with frequencyChange of R with frequency4 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

• 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, Fcr=97700 Hzm2/kg, ’ = 8.1 kg/(m2mm)• s = 10mm, hence = ’s = 8.110 = 81 kg/m2

• fcoinc = Fcr/= 97700/81 = 1206 Hz

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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 Sdiv, and reverberating in room 2, having an equivalent absorption area A2:

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

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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

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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.