Biomedical Engineering Reference
In-Depth Information
For these reasons,
p
and
v
are in general out of phase for generic geometries.
This can be written as a relationship between the pressure
p
and both the
flow
U
and its time derivative as follows:
p
(
t
)=
RU
(
t
)+
I
dU
(
t
)
dt
,
(2.13)
with appropriate coe
cients
R
and
I
. The terms in the equation above will
not contribute equally to the pressure perturbation
p
(
t
)ineverycase.Itmay
happen that in certain circumstances one of them plays a more important
role, while the contribution from the other is negligible. We shall come back
to this subject in Chap. 6.
2.1.2 Mechanisms for Generating Sound
Let us begin by discussing the way in which a siren works [Titze 1994] - one
of the examples mentioned at the beginning of this chapter. This device has
a part that blows air, and a rotating disk with a sequence of holes close to
the edge, as displayed in Fig. 2.1a. The disk faces the mechanism that blows
the air, so that the air jet can pass through one of the holes of the disk. If
the disk is set into a rotating motion (for example, with the help of a motor),
there will be an airflow through the device that is sequentially established
and interrupted as the holes pass in front of the mechanism blowing the air.
Let us imagine the process in detail, taking into account the example of the
cars discussed in Sect. 2.1.1. One of the holes lets an air jet pass through. In
(a)
(b)
(c)
Fig. 2.1.
Different physical phenomena generating sound. (
a
) A siren. An air jet
is blown against a rotating disk with holes. The air jet passes through a hole only
if the hole is just in front of it; otherwise, the jet is interrupted. A pulsating airflow
is established in this way. At a constant rotation speed, the siren produces a note
(a sound of constant frequency), and the frequency of the note is the frequency
at which the holes pass in front of the air jet. (
b
) A recorder. Very close to the
mouthpiece, there is a sharp edge that breaks the otherwise smooth, constant airflow
into vortices, creating turbulence. The frequency of the resulting sound is related
to the effective length of the tube, which can be set by fingering. (
c
) Blowing air
between two sheets of paper. Energy is transferred from the airflow to the sheets of
paper in such a way that a
self-sustained
oscillation of the sheets takes place. This
mechanism is very similar to the one that causes the oscillations of the labia in a
bird's syrinx or the vocal folds in a human larynx
