143
materials can be useful. The impact sound of footsteps can be suppressed using cork, porous rubber, or plastic tiles. On a larger scale,
buildings are isolated by setting the entire structure on resilient
pads such as a composite of rubber filled with cork particles. The
low shear modulus of the rubber isolates the building from shear
waves, and the compressibility of the cork adds a high impedance
to compressive waves.
sound Wave impedance and radiation of sound
energy
If a sound-transmitting material is interfaced with a second one
with different properties, part of the sound wave is transmitted
across the interface, and part is reflected back into the first material.
The transmission and reflection factors are determined by the relative impedances of the two materials. The impedance is defined by
Z
E
= ρ
(4.59)
where E is the appropriate modulus and ρ the density. The reflection and transmission coefficients between Material 1 and Material
2 are given by
R
Z Z
Z Z
T
R
Z
Z Z
=
−
+
= − = +
1
2
1
2
2
1
2
1
2
and
(4.60)
Thus if the two impedances are about equal, most of the sound is
transmitted, but if the impedances differ greatly, most is reflected.
This is the origin of the mass law cited earlier: A heavy wall gives
a large impedance mismatch with air so that most of the sound is
reflected and does not penetrate to the neighboring room.
Table 4.1 lists typical values of the acoustic impedance. In the design
of sound boards (the front plate of a violin, the sound board of a
harpsichord, the panel of a loudspeaker), the intensity of sound
radiation is an important design parameter. Fletcher and Rossing
(1991) and Meyer (1995) demonstrate that the intensity, I, is proportional to the surface velocity and that for a given driving function, this scales with modulus and density as:
I α ρ
E
3
(4.61)
A high value of the combination of properties E ρ
3
, called the
radiation factor, is used by instrument makers to select materials for
sound boards. When the material is elastically anisotropic (as is
wood), E is replaced by E = (E || . E ⊥ ). The last column of Table 4.1
Acoustic Behavior
materials can be useful. The impact sound of footsteps can be suppressed using cork, porous rubber, or plastic tiles. On a larger scale,
buildings are isolated by setting the entire structure on resilient
pads such as a composite of rubber filled with cork particles. The
low shear modulus of the rubber isolates the building from shear
waves, and the compressibility of the cork adds a high impedance
to compressive waves.
sound Wave impedance and radiation of sound
energy
If a sound-transmitting material is interfaced with a second one
with different properties, part of the sound wave is transmitted
across the interface, and part is reflected back into the first material.
The transmission and reflection factors are determined by the relative impedances of the two materials. The impedance is defined by
Z
E
= ρ
(4.59)
where E is the appropriate modulus and ρ the density. The reflection and transmission coefficients between Material 1 and Material
2 are given by
R
Z Z
Z Z
T
R
Z
Z Z
=
−
+
= − = +
1
2
1
2
2
1
2
1
2
and
(4.60)
Thus if the two impedances are about equal, most of the sound is
transmitted, but if the impedances differ greatly, most is reflected.
This is the origin of the mass law cited earlier: A heavy wall gives
a large impedance mismatch with air so that most of the sound is
reflected and does not penetrate to the neighboring room.
Table 4.1 lists typical values of the acoustic impedance. In the design
of sound boards (the front plate of a violin, the sound board of a
harpsichord, the panel of a loudspeaker), the intensity of sound
radiation is an important design parameter. Fletcher and Rossing
(1991) and Meyer (1995) demonstrate that the intensity, I, is proportional to the surface velocity and that for a given driving function, this scales with modulus and density as:
I α ρ
E
3
(4.61)
A high value of the combination of properties E ρ
3
, called the
radiation factor, is used by instrument makers to select materials for
sound boards. When the material is elastically anisotropic (as is
wood), E is replaced by E = (E || . E ⊥ ). The last column of Table 4.1
Acoustic Behavior