In the case of the electromagnetic wave, the {24} amplitude will be the
maximum value to which the electric field attains in either direction,
and the other terms--wave-length, phase, period and frequency--will
have the same meaning as for water ripples.
+Wave Form.+--Waves not only differ in amplitude, wave-length, and
frequency, but also in wave form. Waves may have any form, _e.g._ Fig
12. Or we may have a solitary irregular disturbance such as is caused
by the splash of a stone in water.
[Illustration: FIG. 12.]
But there is one form of motion of a particle in a wave which is looked
upon as the simplest and fundamental form. It is that form which is
executed by the bob of a pendulum, the balance wheel of a watch, the
prong of a tuning-fork, and most other vibrations where the controlling
force is provided by a spring or by some other elastic solid.
It is called "Simple Harmonic Motion" or "Simple Periodic Motion," and
the essential feature of it is that the force restoring the displaced
particle to its undisturbed position is proportional to its
displacement from the undisturbed position. A wave in which all the
particles execute simple harmonic motion has the form in Fig. 10 or
Fig. 11, which is therefore looked upon as the fundamental wave form or
simple wave form.
Simple waves will vary only in amplitude, wave-length, and frequency,
and the energy in the wave will depend upon these quantities.
{25}
+Energy in a Simple Wave.+--If the velocity is the same for all
wave-lengths, then the frequency will evidently be inversely
proportional to the wave-length and the energy will depend upon the
amplitude and the wave-length. The kinetic energy of any moving body,
_i.e._ the energy due to its motion, is proportional to the square of
its velocity, and we may apply this to the motion of the particles in a
wave and to show how the energy depends upon the amplitude and
wave-length.
Since the distance travelled by a particle in a single period of the
wave will be equal to four times the amplitude, the velocity at any
point in the wave must be proportional to the amplitude and therefore
the kinetic energy is proportional to the square of the amplitude.
With the same amplitude but with different wave-lengths, we see that
the time in which the oscillation is completed is proportional to the
wave-length and that the velocity is therefore inversely proportional
to the wave-length. The kinetic energy is therefore inversely
proportional to the square of the wave-length.
Public-domain text, read in full here on John Shaqi.
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