WHAT IS A WAVE?
from The Evolution of Physics
by Albert Einstein and Leopold Infeld
A bit of gossip starting in London reaches Edinburgh
very quickly, even though not a single individual
who takes part in spreading it travels between these
two cities. There are two quite different
motions involved, that of the rumor, London to Edinburgh,
and that of the persons who spread the rumor.
The wind, passing over a field of grain, sets up a wave
which spreads our across the whole field. Here again
we must distinguish between the motion of the wave
and the motion of the separate plants, which undergo
only small oscillations. We have all seen the waves that
spread in wider and wider circles when a stone is thrown
into a pool of water. The motion of the wave
is very different from that of the particles of water.
The particles merely go up and down.
The observed motion of the wave is that of a state
of matter and not of matter itself. A cork floating on
the wave shows this clearly, for it moves up and down
in imitation of the actual motion of the water, instead
of being carried along by the wave.
In order to understand better the mechanism of the wave
let us again consider an idealized experiment.
Suppose that a large space is filled quite uniformly
with water, or air, or some other "medium". Somewhere in
the centre there is a sphere. At the beginning of the
experiment there is no motion at all. Suddenly the
sphere begins to "breathe" rhythmically, expanding and
contracting in volume, although retaining its spherical
shape. What will happen in the medium?
Let us begin our examination at the moment the
sphere begins to expand. The particles of the medium in the
immediate vicinity of the sphere are pushed out, so that the
density of a spherical shell of water, or air, as the case
may be, is increased above its normal value.
Similarly, when the sphere contracts, the density of that
part of the medium immediately surrounding it will be decreased.
These changes of density are propagated throughout the
entire medium. The particles constituting the medium perform
only small vibrations, but the whole motion is that of a
progressive wave.
The essentially new thing here is that for the first time we
consider the motion of something which is not matter,
but energy propagated through matter. Using the example of
the pulsating sphere, we may introduce two general physical
concepts, important for the characterization of waves.
The first is the velocity with which the wave spreads.
This will depend on the medium, being different for water
and air, for example. The second concept is that of
wavelength. In the case of waves on a sea or river it is
the distance from the trough of one wave to that of the
next, or from the crest of one wave to that of the next.
Thus sea waves have greater wave-length than river waves.
In the case of our waves set up by a pulsating sphere the
wave-length is the distance, at some definite time, between
two neighboring spherical shells showing maxima or minima
of density. It is evident that this distance will not depend
on the medium alone. The rate of pulsation of the sphere
will certainly have a great effect, making the wave-length
shorter if the pulsation becomes more rapid, longer if the
pulsation becomes slower.
This concept of a wave proved very
successful in physics. It is definitely a mechanical concept.
The phenomenon is reduced to the motion of particles which,
according to the kinetic theory, are constituents of
matter. Thus every theory which uses the concept of
wave can, in general, be regarded as a mechanical theory.
For example, the explanation of acoustical phenomena is
based essentially on this concept. Vibrat- ing bodies,
such as vocal cords and violin strings, are sources of
sound waves which are propagated through the air in the
manner explained for the pulsating sphere. It is thus
possible to reduce all acoustical phenomena to mechanics
by means of the wave concept. It has been emphasized
that we must distinguish between the motion of the particles
and that of the wave itself, which is a state of the medium.
The two are very different, but it is apparent that in
our example of the pulsating sphere both motions take
place in the same straight line. The particles of the medium
oscillate along short line segments, and the density increases
and decreases periodically in accordance with this motion.
The direction in which the wave spreads and the line
on which the oscillations lie are the same. This type of
wave is called longitudinal. But is this the only kind
of wave? It is important for our further considerations
to realize the possibility of a different kind of wave,
called transverse. Let us change our previous example.
We still have the sphere, but it is immersed in a medium
of a different kind, a sort of jelly instead of air or water.
Furthermore, the sphere no longer pulsates but rotates
in one direction through a small angle and then back again,
always in the same rhythmical way and about a definite
axis. The jelly adheres to the sphere and thus the
adhering portions are forced to imitate the motion.
These portions force those situated a little farther
away to imitate the same motion, and so on, so that a
wave is set up in the medium. If we keep in mind the
distinction between the motion of the medium and the motion
of the wave, we see that here they do not lie on the same
line.
The wave is propagated in the direction of the radius of
the sphere, while the parts of the medium move
perpendicularly to this direction. We have thus
created a transverse wave.
Waves spreading on the surface of water are
transverse. A floating cork only bobs up and down, but the
wave spreads along a horizontal plane. Sound waves,
on the other hand, furnish the most . . .
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