42.3 Sound-Absorbing Materials

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42.3.1 Porous Material

Porous acoustical materials are a special category of a more general class of gas – solid mixtures. They

range from porous solids, for example, porous rocks, fibrous granular solids, expanded plastics, and form

materials, to porous or turbid gases, for example, suspensions and emulsions. Sound is attenuated in a

gas-saturated porous solid due to the restriction on the gas movement within it. A convenient

microstructure model for such materials is one of a rigid solid matrix through which run cylindrical,

capillary pores (tubing) with constant radius, normal to its surface. This model enables the use of

Kirchoff ’s theory of sound propagation in narrow tubes with rigid walls. Accordingly, this mechanism of

dissipation may be identified as (1) a viscous loss in the boundary layer at the wall of each capillary tube

Design of Absorption 42-3

© 2005 by Taylor & Francis Group, LLC

associated with the relative motion between the viscous gas and the solid wall, or (2) heat conduction

between compressions and rarefactions of the gas and the conducting solid walls.

42.3.2 Tubular Material

Consider the absorption of low-frequency sound using the tubular absorbing material. By itself, sound

absorption is not satisfactory with the tubular absorbing material. The material produces bending

vibration due to an acoustic wave through it, and sound absorption occurs by the internal friction of the

material. For hard plywood and gypsum boards, there is a natural frequency in the range 100 to 200 Hz,

and the absorption coefficient ranges from 0.3 to 0.5. It is possible to increase the absorption coefficient

by coating the board surface with fibrous absorbing material.

42.3.3 Membrane Material

For membrane material, the sound-absorption mechanism makes use of resonant vibration. Hence,

resonant frequency is a governing parameter. The imaginary part (the reactance term) of the acoustic

impedance of a membrane gives rise to a resonance. The associated natural frequency is given by

fr ¼

1

2

1

m

1:4 £ 105

L

􀁻 !

þ Km

( )

ð42:10Þ

where

fr ¼ natural frequency (Hz)

m ¼ surface density (kg/m2)

L ¼ thickness of air space (m)

Km ¼ board rigidity (kg/m2 sec2)

The Km values of some boards are shown in Figure 42.2. The absorption coefficient is approximately 0.3

to 0.4 in the frequency range of 300 to 1000 Hz, when the thickness of the air space between the

membrane and the rigid wall behind it is 50 to 100 mm.

42.3.4 Perforated Plate

A perforated board of sound absorbing material (i.e., a board with holes) is placed over a rigid wall at a

fixed clearance, as shown in Figure 42.3. The sound-absorption characteristics depend on the board

thickness, t; the hole diameter of the perforations, d; the clearance, L; between the perforated board and

the rigid wall, and so on. The absorption coefficient becomes a maximum at resonant frequency. In the

present case, the resonant frequency is given by

fr ¼

c

2p

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

ðt þ 0:8dÞL

r

ð42:11Þ

where sound speed is c; the airspace thickness is L (typically, 300 mm or less), and the ratio of the total

area of holes to the total area of the board is 1: The absorption coefficient is approximately 0.3 to 0.4.

42.3.5 Acoustic Resonator

Yet another method of achieving sound absorption is using an acoustic resonator of Helmholtz type,

which consists of a vessel of any shape containing a volume air, as shown in Figure 42.4. The air

volume is in direct communication with the ambient air in the room through an interconnecting tube,

which may be long or short and of any cross-sectional shape. An example of a resonator of Helmholtz

type may be a 1 gal jar. When a sound wave impinges on the aperture of neck of the jar, the air in

the neck will be set in oscillation, periodically expanding and compressing the air in the vessel.

42-4 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

The resulting amplified motion of the air particles in the neck of the jar, due to phase cancellation

between the air plug in the neck and the air volume in the vessel, causes energy dissipation due to

friction in and around the neck. This type of absorber can be designed to produce maximum

absorption over a very narrow frequency band or even a wide frequency band. The resonant frequency

of a Helmholtz resonator may be expressed as

fr ¼

c

2m

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

ðt þ 0:8dÞL

r

ð42:12Þ

where

c ¼ speed of sound (m/sec)

Sn ¼ cross-sectional area of neck of jar (m2)

dn ¼ diameter of neck of jar (m)

V ¼ volume of vessel (m3)

Vinyl sheet

(1) Back air space 50 mm

(2) back air space 105 mm

(2)

(1)

0.4

0.2

0

102 103 104

Frequency (Hz)

a

(b)

(a)

FIGURE 42.2 Some Km values for membrane absorbing materials.

Design of Absorption 42-5

© 2005 by Taylor & Francis Group, LLC

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