Waves and ripples in water, air, and æther : $b Being a course of Christmas lectures delivered at the Royal Institution of Great BritainFleming, J. A. (John Ambrose), Sir
Science
Waves and ripples in water, air, and æther : $b Being a course of Christmas lectures delivered at the Royal Institution of Great Britain
Fleming, J. A. (John Ambrose), Sir
Electric waves; Sound; Waves
Or, look at a train of sea waves. Some parts of the water are at any
moment lifted high above the average level of the sea, or are much
below it, but are otherwise nearly at rest. These portions possess
what is called potential energy, or energy of position. Other parts
of the water are at the average level of the sea, but are moving with
considerable velocity, and these portions possess energy of motion.
Every other part of the wave has in some degree both energy of motion
and energy of position, and it can be shown that the energy of the
whole wave is half of one kind and half of the other.
As a wave progresses over the surface, wave-energy is continually being
imparted to portions of the water in front, and it is transferred away
from others in the rear. In the very act of setting a fresh particle
of water in oscillation, the portions already vibrating must diminish
their own motion. They may hand on the _whole_ of their energy or
only a _part_ of it to their neighbours. This distinction is a very
important one, and it determines whether a single act of disturbance
shall create a _solitary wave_ or _wave-train_ in a medium.
[Illustration: FIG. 12.]
The difference may be illustrated as follows: Consider a row of glass
or steel balls suspended by threads so hung as to be quite close to
each other (see Fig. 12). Withdraw the first ball, and let it fall
against the second one. The result is that the last ball of the row
flies off with a jerk. In this case the whole energy imparted to the
first ball is transmitted along the row of balls. The first ball, on
falling against the second one, exerts on it a pressure which slightly
squeezes both out of shape. This pressure is just sufficient to bring
the first ball to rest. The second ball, in turn, expands after the
blow and squeezes the third, and so on. Hence, in virtue of Newton’s
Third Law of Motion, that “action and reaction are equal and opposite,”
it follows that the pressure produced by the blow of the first ball is
handed on from ball to ball, and finally causes the last ball to fly
off.
In this case, owing to the rigid connection between the elastic balls,
each one hands on to its neighbour the whole of the energy it receives.
Supposing, however, that we separate the balls slightly, and give the
first ball a transverse, or side-to-side swing. Then, owing to the fact
that there is no connection between the balls, the energy imparted to
the first ball would not be handed on at all, and no wave would be
propagated.
Between these two extremes of the whole energy transferred and a
solitary wave produced, and no energy transferred and no wave produced,
we have a condition in which an initial disturbance of one ball gives
rise to a wave-train and part of the energy is transferred.
Public-domain text, read in full here on John Shaqi.
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