A Reading from Albert Einstein's The Evolution of Physics


   
 
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 .  .  .

Read more online in pdf fulltext or eBook formats -
click here and go to page 104
 
 
Thanks and kudos to archive.org for having this wonderful 
book available to read online. I found a paperback version 
at the North Berkeley library and I'm reading it now. 
 
A great book with some behind the scenes 
info on Mr. Infeld and Banish Hoffmann (who wrote a couple 
of books I really like including The Tyranny of Tests). 
 
The Evolution of Physics is written so that both 
a physicist and a layman can enjoy it. 
 
Of course, I really like the chapter on light and 
the chapter on Maxwell's equations.