E MOTION. General.--In nature there are two types of recurrent motion,
somewhat closely connected mathematically, in which repetition of motion
occurs at regular intervals.

"One type of this motion, in cycles as we may say, repeats the motion in
one place, and is in a sense stationary. The tuning fork in motion moves
through the same space again and again; a similar movement is the motion
of a vibrating string. Of this stationary type may be mentioned the
heartbeats, the pulse, the respiration, the tides, and the rotation of a
wheel about its axis.

"The second type of recurrent motion transmits or carries the vibratory
impulse over an extent of space as well as time. The waves of the sea are
of this character. Sound waves, electrical vibrations or waves, and
radiant energy vibrations are transmitted by a process similar to that by
which the waves of the sea are carried.

"Both of these types of motion are representable mathematically by
equations involving a sequence of trigonometric functions. To the
fundamental and basic function involved, _y_ = sin _x_, we will direct our
attention in the next section and to simple applications in other sections
of this chapter....

"Sound Waves.--If a tuning fork for note lower C is set to vibrating, the
free bar makes 129 complete, back-and-forth, vibrations in one second. By
attaching a fine point to the end of the bar and moving under this bar at
a uniform rate, as it vibrates, a smoke-blackened paper, a sinusoidal
curve is traced on the paper. Our curve is traced by a bar vibrating 50
times in 1 second.

[ A graph, showing a wavy line. "Tuning fork vibrations recorded on smoked
paper." ]

Tuning fork vibrations recorded on smoked paper.

"Corresponding to each movement of the vibrating rod there is a movement
of the air. As the bar moves to the right it compresses the layer of air
to its right and that _compression_ is immediately communicated to the
layer of air to the right; as the bar moves back and to the left, the
pressure on the adjacent air is released and a _rarefaction_ takes place.
In 1/50 of 1 second you have the air adjacent to the rod _compressed_,
back to normal, and _rarefied_; during this time the neighboring air is
affected and the compression is communicated a distance which is the _wave
length_ of this given sound wave. In 1 second this disturbance is
transmitted 1100 feet at 44 deg. Fahrenheit. The wave length for this sound
wave then is 1100/50 =