Geography Reference
In-Depth Information
7.3.1
Acoustic or Sound Waves
Sound waves, or acoustic waves, are
longitudinal waves
. That is, they are waves in
which the particle oscillations are parallel to the direction of propagation. Sound is
propagated by the alternating adiabatic compression and expansion of the medium.
As an example, Fig. 7.5 shows a schematic section along a tube that has a diaphragm
at its left end. If the diaphragm is set into vibration, the air adjacent to it will be
alternately compressed and expanded as the diaphragm moves inward and outward.
The resulting oscillating pressure gradient force will be balanced by an oscillating
acceleration of the air in the adjoining region, which will cause an oscillating
pressure oscillation further into the tube, and so on. The result of this continual
adiabatic increase and decrease of pressure through alternating compression and
rarefaction is, as shown in Fig. 7.5, a sinusoidal pattern of pressure and velocity
perturbations that propagates to the right down the tube. Individual air parcels do
not, however, have a net rightward motion; they only oscillate back and forth while
the pressure pattern moves rightward at the speed of sound.
To introduce the perturbation method we consider the problem illustrated by
Fig. 7.5, that is, one-dimensional sound waves propagating in a straight pipe par-
allel to the x axis. To exclude the possibility of
transverse
oscillations (i.e., oscil-
lations in which the particle motion is at right angles to the direction of phase
propagation), we assume at the outset that v
=
w
=
0. In addition, we eliminate
all dependence on y and z by assuming that u
u(x,t). With these restrictions the
momentum equation, continuity equation, and thermodynamic energy equation
for adiabatic motion are, respectively,
=
Du
Dt
+
1
ρ
∂p
∂x
=
0
(7.6)
Fig. 7.5
Schematic diagram illustrating the propagation of a sound wave in a tube with a flexible
diaphragm at the left end. Labels H and L designate centers of high and low perturbation
pressure. Arrows show velocity perturbations. (b) The situation 1/4 period later than in (a)
for propagation in the positive x direction.
