Biomedical Engineering Reference
In-Depth Information
the neighborhood of the hole, we have a high density of air. This injection of
air will stop as soon as the disk rotates a little, such that the hole no longer
faces the mechanism blowing the air. If the propagation speed of the sound
is high with respect to the speed of the holes, by the time new air injection
takes place, the air density in the neighborhood of the hole will be similar
to the density that we had at the beginning of the process. The recurrent
passing of holes in front of the air jet as the disk rotates then generates a
note. The frequency of such a note will be the frequency at which the holes
pass in front of the air jet. For example, if the disk rotates at such a speed
that 261 holes pass in front of the air jet per second, then the frequency of
the note is 261 Hz (the middle C).
The flute works in a different way. It consists of an open tube made of
wood or metal, which becomes narrow close to one end: the end through
which we blow air. As the air goes into the tube through this end, it en-
counters a sharp edge (Fig. 2.1b). The role of this edge during the onset of
the sound generation process is to divide the airflow and generate turbulence:
the laminar flow loses stability, giving rise to vortices (known as
eolian noise
)
that travel downstream along the tube. After this initial process, the jet will
alternately leave the edge above or below, owing to a mechanism that in-
volves waves being generated in the tube, giving rise to density fluctuations
of a definite frequency. In the siren, a time-varying flow is generated by a
mechanical process, while in the flute, a time-varying flow is present because
the constant, laminar flow loses stability with respect to a time-fluctuating
regime.
It is worthwhile to think about a third example: blowing air between
two sheets of paper (Fig. 2.1c). If the sheets are not too large (for instance,
one-quarter of a letter- or A4-sized sheet), a good vibrating effect can be
achieved. A similar way to obtain a good sound, however, is to cut a piece of
paper and hold it between the fingers, as shown in Fig. 2.2. As we blow, we
can feel in our lips the paper vibrating, and hear a high-pitched sound. The
mechanism by which the sound is produced is not trivial. In fact, it shares
many elements with the process involved in the generation of sound in the
avian vocal organ. For this reason, we shall analyze this process later. For now
it is enough to say that, as in the example of the siren, the sound is produced
by temporal fluctuations in the airflow due to periodic obstructions. However,
in one important aspect, the physics of this problem is more complicated than
that involved in the siren. In the case of the sheets of paper, the periodic
obstructions to the airflow are not produced by an “external” motion (such
as the rotation of a disk). Instead, energy is transferred from the airflow
to the sheets of paper, establishing an oscillatory regime. These oscillations,
partially and in a periodic fashion, obstruct the flow. The origin of the sound
produced is the creation of local density fluctuations that originate in the
presence of a time-varying airflow.
