Introduction to Acoustics

996 Part G Structural Acoustics and Noise
Part G 23.3
will be discussed, methods of measurement of normal
impedance will be presented, and some results of
calculations on composite structures will be shown.
A key parameter is the flow resistance r which can be
defined as the ratio of the pressure drop across a sample
of a material and the velocity through it
r = ∆p
. (23.44)
u
The flow resistance is usually measured for steady flow
through the material, the assumption being made that
this value is equivalent, at least at low frequencies, for
the particle velocity in a sound wave.
The unit of of flow resistance is N s/m3 , the
MKS Rayl. Actual values are often specified as a dimensionless
quantity, the specific flow resistance rs,
where rs = r/ρc = r/406 for a density of air ρ of
1.18 kg/m3 and a speed of sound c of 344 m/s. It is also
common to specify the flow resistance per unit thickness.
Another property of sound-absorptive materials is
that they can often considered to be locally reacting.
When a sound wave is incident on a locally reacting material,
the local pressure at the surface produces a particle
velocity normal to the surface. When the two are sinusoidal
and expressed as complex numbers the ratio is the
normal impedance of the surface
zN = p
. (23.45)
u
The normal impedance is independent of the angle of
incidence of the sound wave.
Two mechanisms are mainly responsible for the absorption
of sound. First, friction in the boundary layer
between the air and the internal structure of the material
absorbs energy, and a large particle velocity is needed
for effective absorption. Second, the temperature rise
during the compression phase of the sound wave results
in conduction of heat into the material, further absorbing
energy from the sound wave. The former is generally
most important.
The sound absorption coefficient α is the ratio of the
sound energy absorbed by the surface and the incident
sound energy. In general, it is a function of the angle of
incidence of the sound wave on the material. It varies
from 0 to 1.0, although some measurement methods –
described later in the section – result in values of α>1.
The unit of sound absorption is the metric Sabine, S.
Material with an area of 1 m 2 and α = 1 has 1 Sabine
of sound absorption (10.8 Sabins in English units). The
sound-absorptive properties of, for example, hanging
baffles are frequently expressed in Sabins.
Normal incidence absorption coefficient
1.0
0.8
0.6
0.4
0.2
0.0
100
1000
λ/4 3λ/4 5λ/4
10000
Frequency (Hz)
Fig. 23.23 Normal incidence sound absorption coefficient
for a thin, rigid sound absorber having a flow resistance ρc
placed 50 mm from a rigid termination. Calculated using
a program by Ingard [23.125]
Sound absorption coefficients are frequently measured
in octave bands, and the noise reduction coefficient
(NRC) is the average absorption in the 250, 500, 1000,
and 2000 Hz octave bands.
The importance of particle velocity can be illustrated
for the case where a thin sound absorber having a flow
resistance ρc is placed in a tube at a distance 50 mm from
a rigid termination. The normal incidence absorption coefficient
calculated as a function of frequency is shown in
Fig. 23.23. It can be seen that the absorption coefficient
is highest when the distance from the rigid termination is
an odd multiple of one-quarter wavelength of the sound.
It is at these distances that the particle velocity in the
absorber is highest.
Galaitsis [23.126] showed that multiple resistive
sheets can be used to improve the sound absorption
at normal incidence, and Ingard [23.125] extended the
analysis to diffuse fields for both locally and non-locally
reacting materials. As an example, Fig. 23.24 shows the
absorption coefficients for two resistive sheets having
a flow resistance 1.5 ρc and a total absorber thickness
of 50 mm. The first sheet is 33 mm from a rigid surface,
and the spacing between the two sheets is 17 mm. The
structure can be made approximately locally reacting by,
for example, using a honeycomb material between the
resistive layers.
Most sound-absorptive materials are relatively thick
(e.g., 25 mm), and in this case, it is beneficial to have
an air gap behind the material when it is mounted
near a rigid surface. In the figure below, the sound-