Sound absorbers - Building Acoustics - page 200

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

⎧

2

⎫

⎛ ⎞

⎛ c ⎞

⎪ ⎪ 1

0
eff

y = Re as a function of ⎜ ⎟ , a linear function given by

⎨ ⎜ ⎟ ⎬

⎜ ⎟

c

f

⎪ ⎝ ⎠ ⎪

⎝ ⎠

⎩ ⎭

⎡ ⎤

⎛ ⎞

1 μ 1 γ − 1

yk ≈+ 1 + . (5.73)

⎢ ⎥

⎜ Λ ⎟ s

ρπ ′

f Pr Λ

⎢ ⎝ ⎠ ⎥

⎣ ⎦

0

1.50

1.45

1.40

1.35

1.30

Helium

1.25

1.20

1.15

Air

1.10

1.05

1.00

0.000 0.001 0.002 0.003 0.004

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

Figure 5.35 The relationship between the real part of (c 0 /c eff ) 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 k S . Material parameters: r − 30000Pa⋅s/m 2 , σ − 0.95, Λ − 50μm, Λ′ − 100μm. 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

−
=+

⎡ 1 γ 1 ⎤

L ,

⎢ ⎥

Λ ′

Pr Λ

⎣ ⎦

whereas k S 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 b air and b He given by