Biomedical Engineering Reference
In-Depth Information
Maybe the person that began this process finds the spectacle of a propa-
gating “push” amusing, and repeats it from time to time (trying to implement
this thought experiment is not the best idea). The time between “pushes” is
what we call the
period
of the
perturbation
. A related concept is the
frequency
:
the number of pushes per unit of time (for example, “pushes” per second).
Within our metaphor, each subject can either experience a slight deviation
from his/her position of equilibrium or be close to falling. The quantity that
describes the size of the perturbation is called its
amplitude
.
From this metaphor, we can extract the fact then that it is possible to
propagate energy (capacity to do work) through a medium (a group of people
standing in line) that undergoes perturbations on a local scale (no one moves
far away from their equilibrium position), owing to a generator of perturba-
tions (the last person in line, the one with a curious sense of humor) that
produces a signal (a sequence of pushes) of a given amplitude and at a certain
frequency.
1.1.2 Getting Serious
While it is true that metaphors can help us construct a bridge between a
phenomenon close to our experience and another one which requires indirect
inferences, it is also true that holding on to them for too long can hinder
us in our understanding of nature. Sound is a phenomenon of propagative
character, as in the situation described before. But an adequate description
of the physics involved must consider carefully the properties of the real
propagative medium, which, in the present case of interest, is air.
If an object moves slowly in air, a smooth flow is established around it. If
the movement is so fast that such a flow cannot be established, compression
of the air in the vicinity of the moving object takes place, causing a local
change in pressure. In this way, we can originate a propagative phenomenon
like the one described in our metaphor. In order to establish sound, the excess
pressure must be able to push the air molecules in its vicinity (in terms of
our metaphor, the people in the line should not be more than approximately
an arm's length away from each other). Can we state a similar condition for
the propagation of sound in air?
As opposed to what happens in our metaphor, the molecules of air are
not static, or in line. On the contrary, they are moving and colliding with
each other in a most disorderly manner, traveling freely during the time
intervals between successive collisions. The average distance of travel between
collisions is known as the
mean free path
. Therefore, if we establish a high
density of molecules in a region of space, the escaping particles will push the
molecules in the region of low density only if the density varies noticeably
over distances greater than the mean free path. If this is not the case, the
region of high density will “smoothen” without affecting its vicinity. For
this reason, the description of sound is given in terms of the behavior of
“small portions of air” and not of individual molecules. Here is an important
