Civil Engineering Reference
In-Depth Information
1.00
0.10
0.01
0
100
200
300
400
500
Frequency (Hz)
Figure 3.17
Relative sound pressure at a fixed position,
x
= 1.2 m, in the tube shown in
Figure 3.16.
Solid line -
source at
x
0
= 0.5 m. Dashed line - source at
x
0
= 0.85 m (centre of tube).
3.7
WAVE TYPES IN SOLID MEDIA
As mentioned in the introduction to this chapter, acoustic waves in solid media are
distinctly different from their counterpart in fluids due to shear stresses and shear
deformations. This leads to the occurrence of several other wave types besides the
compressional or longitudinal treated up to now. We shall mainly give an outline of these
wave types but go into some detail on bending or flexural waves, the wave type of
particular importance in sound transmission phenomena in buildings.
Two types of wave may exist at the same time in a medium of infinite extent; ideal
longitudinal waves, as in fluids, and ideal transverse or shear waves. In the latter, the
particle displacement will be normal to the direction of propagation; see below. From the
basic equations of elasticity we may show that all wave motion in solids may be seen as a
combination of these two “pure” waves but many of these combinations have specific
names. It could be mentioned that in a semi-infinite medium surface waves (Rayleigh
waves) may occur but these have little relevance in building acoustics. We shall be more
interested in which combinations of the two basic waves may exist in structural elements
such as beams and plates, an example being the aforementioned bending waves.
3.7.1
Longitudinal waves
Ideal or pure longitudinal waves may only exist in a medium of infinite extent.
Practically speaking, this implies that the solid structure must be very large compared
with the wavelength. When taking into account the actual dimensions of building
elements and the relevant frequency range, displacements normal to the direction of
