141
electrons (β-particles) released by a mildly radioactive ingredient
in the paint.
4.8 aCoustiC Behavior
The human ear responds to frequencies from 20 Hz to about
20,000 Hz, corresponding to wavelengths in air between 17 m and
17 mm. The range of acoustic frequency is far greater than this (see
Figure 4.71), with wavelengths that extend into the nanorange.
The vibrations that cause sound produce a change of air pressure
in the range 10
−4 Pa (low-amplitude sound) to 10 Pa (the threshold of pain). It is usual to measure this on a relative, logarithmic
scale, with units of decibels (dB). The decibel scale compares two
sound intensities using the threshold of hearing as the reference level
(0 dB).
sound velocity and Wavelength
The sound velocity in a long rod of a solid material (such that the
thickness is small compared with the wavelength) is
ν
ρ
1 =
E
(4.57)
where E is Young’s modulus and p is the density. If the thickness of
the rod is large compared with the wavelength, the velocity instead
is
ν
ν
ν ν ρ
B
E
=
−
(
)
− −
(
)
1
1
2
2
where v is Poisson’s ratio. These two sound velocity values don’t
differ much—a maximum of 25% at most.
Elastically anisotropic solids (fiber composites such as CFRP and all
woods are anisotropic) have sound velocities that depend on direction. If E || is the modulus along the direction of the fibers or grain
and E ⊥ is that perpendicular to it, the ratio of the two velocities, as
given by Equation 4.57, is
ν
ν
⊥
⊥
=
E
E
(4.58)
sound Management
The mechanism for reducing sound intensity within a given
enclosed space (a room, for instance) depends on where the sound
Figure 4.71
The acoustic spectrum from the extreme ultrasonic
to the seismic, a range of 10
8
. The audible part
is a thick slice of this range. The figure is based
on acoustic waves in air, velocity 350 m/s; for
water, shift the wavelength scale up relative to the
frequency scale by a factor of 3; for rock, shift it
up by a factor of 10.
Wavelength (m)
10 3
1
10 -6
10 -3
Seismology
Ultra long-range sonar
Frequency (Hz)
10 6
10 9
10 3
1
Long-range sonar
Sea-floor mapping sonar
Audible range
Acoustic microscopy
Surface scanners
Bats, dolphins, whales
Middle C
Medical CT scanners
20 Hz
20 kHz
Acoustic Behavior
electrons (β-particles) released by a mildly radioactive ingredient
in the paint.
4.8 aCoustiC Behavior
The human ear responds to frequencies from 20 Hz to about
20,000 Hz, corresponding to wavelengths in air between 17 m and
17 mm. The range of acoustic frequency is far greater than this (see
Figure 4.71), with wavelengths that extend into the nanorange.
The vibrations that cause sound produce a change of air pressure
in the range 10
−4 Pa (low-amplitude sound) to 10 Pa (the threshold of pain). It is usual to measure this on a relative, logarithmic
scale, with units of decibels (dB). The decibel scale compares two
sound intensities using the threshold of hearing as the reference level
(0 dB).
sound velocity and Wavelength
The sound velocity in a long rod of a solid material (such that the
thickness is small compared with the wavelength) is
ν
ρ
1 =
E
(4.57)
where E is Young’s modulus and p is the density. If the thickness of
the rod is large compared with the wavelength, the velocity instead
is
ν
ν
ν ν ρ
B
E
=
−
(
)
− −
(
)
1
1
2
2
where v is Poisson’s ratio. These two sound velocity values don’t
differ much—a maximum of 25% at most.
Elastically anisotropic solids (fiber composites such as CFRP and all
woods are anisotropic) have sound velocities that depend on direction. If E || is the modulus along the direction of the fibers or grain
and E ⊥ is that perpendicular to it, the ratio of the two velocities, as
given by Equation 4.57, is
ν
ν
⊥
⊥
=
E
E
(4.58)
sound Management
The mechanism for reducing sound intensity within a given
enclosed space (a room, for instance) depends on where the sound
Figure 4.71
The acoustic spectrum from the extreme ultrasonic
to the seismic, a range of 10
8
. The audible part
is a thick slice of this range. The figure is based
on acoustic waves in air, velocity 350 m/s; for
water, shift the wavelength scale up relative to the
frequency scale by a factor of 3; for rock, shift it
up by a factor of 10.
Wavelength (m)
10 3
1
10 -6
10 -3
Seismology
Ultra long-range sonar
Frequency (Hz)
10 6
10 9
10 3
1
Long-range sonar
Sea-floor mapping sonar
Audible range
Acoustic microscopy
Surface scanners
Bats, dolphins, whales
Middle C
Medical CT scanners
20 Hz
20 kHz
Acoustic Behavior