Civil Engineering Reference
In-Depth Information
CHAPTER 3
Waves in fluid and solid media
3.1
INTRODUCTION
This chapter is devoted to the fundamental properties of waves in fluids as well as in
solid media, the latter being metal, concrete, plastics etc. Concerning fluid media we
shall be considering gases only, which in normal cases in building acoustics will be air.
In addition to the treatment of the various types of wave motion we shall deal with
the way waves are generated, i.e. examine sound sources and the way we can calculate
the sound field generated by these sources. Furthermore, we shall use some simple cases
of sound reflection from surfaces as an introduction to the later treatment of sound
absorption and sound transmission.
As pointed out earlier, a wave is characterized by an oscillating motion propagated
through the actual medium by virtue of its physical characteristics. Energy is transported
by the wave but there is no net transfer of the medium. This does not imply that the
medium, in a global sense, cannot be transported along with the wave, e.g. by wind, air
movement in a ventilation duct etc. We shall, however, limit the treatment to cases where
the medium is at rest.
Sound waves in solids can, as opposed to sound waves in fluids, store energy in
shear motion. Whereas only compressional waves can exist in fluids, several other types
of wave and combinations thereof are possible in solids. Of special importance in sound
transmission in buildings is
bending waves
, also called
flexural waves
. Bending waves in
plate-like structures will therefore be an important subject.
We shall presuppose that the acoustic phenomena are linear. Simply stated, this
implies that the excursions in value of the physical quantities during wave motion are
small compared with the value in a state of equilibrium. Non-linear phenomena occurring
due to large deformations or at very high pressures are outside the scope of this topic.
3.2
SOUND WAVES IN GASES
A sound wave propagating through a gas gives space and time variations in pressure,
density and temperature as well as relative displacement from equilibrium of the particles
of the gaseous medium. Observing the instantaneous values of pressure, density and
particle velocity we may split these into an equilibrium part (or “direct current” part) and
a fluctuating part due to the wave. We may write
PPp
=
+
,
ρ
=
ρρ
+
,
and
v=V+v
,
(3.1)
total
0
total
0
total
0
where
P
0
and ρ
0
are the equilibrium value for the pressure (the atmospheric pressure) and
density, respectively. The acoustic “disturbances” are the
sound pressure
p
and the
density variation
ρ. Given the loudness of sound we are normally exposed to means that
