Building Acoustics

200 Building acoustics

determination of the characteristic viscous and thermal lengths. A procedure to do this is
to plot the quantity

2

0

eff

1

Re as a function of ,

c

y

c f

⎧⎫⎪⎪⎛⎞ ⎛⎞

= ⎨⎬⎜⎟ ⎜⎟

⎪⎪⎝⎠ ⎜⎟

⎩⎭ ⎝⎠

a linear function given by

(^) s
0

111

1

Pr

yk

f

μγ

ρπ

⎡⎤⎛⎞−

≈+⎢⎜+

Λ

⎟⎥.

⎢⎥⎣⎦⎝⎠Λ′

(5.73)

0.000 0.001 0.002 0.003 0.004

Square rot of inverse frequency((1/Hz)1/2)

1.00

1.05

1.10

1.15

1.20

1.25

1.30

1.35

1.40

1.45

1.50

Real part of (

c/

ceff

(^2) )
/k
s
Helium
Air
Figure 5.35 The relationship between the real part of (c 0 /ceff )^2 and the square root of the inverse frequency for
a porous material having air-filled and helium-filled pores, respectively. The ordinate is normalized by the
tortuosity kS. Material parameters: r − 30000Pa⋅s/m^2 , σ − 0.95, Λ − 50 μm, Λ′ − 100 μm. Solid lines – complete
model. Dashed lines – approximate model.
The slope of this function gives the possibility of determining the length L in the
expression
1
11
,
Pr

L

γ

−

⎡ − ⎤

=+⎢ ⎥

⎣Λ Λ′⎦

whereas kS again is determined by the intercept with the ordinate. Performing this
measurement twice, once by having the pores filled with air and, second, by helium, we
can determine Λ and Λ′ by finding the slopes bair and bHe given by