A transverse wave
is a wave in which the particles of the medium are
displaced in a direction perpendicular to the direction
of energy transport. A transverse wave can be created in
a rope if the rope is stretched out horizontally and the
end is vibrated back-and-forth in a vertical direction.
If a snap-shot of such a transverse wave could be taken
so as to freeze the shape of the rope in time,
then it would look like the following diagram.
The dashed line drawn through the
center of the diagram represents the equilibrium
or rest position of the string. This is the position
that the string would assume if there were no disturbance
moving through it. Once a disturbance is introduced into
the string, the particles of the string begin to vibrate
upwards and downwards. At any given moment in time, a
particle on the medium could be above or below the rest
position. Points A and F on the diagram represent the
crests of this wave. The
crest of a wave is
the point on the medium which exhibits the maximum amount
of positive or upwards displacement from the rest
positon. Points D and I on the diagram represent the
troughs of this wave. The
trough of a wave is
the point on the medium which exhibits the maximum amount
of negative or downwards displacement from the rest
positon.
The wave shown
above can be described by a variety of properties. One
such property is amplitude. The
amplitude of a wave
refers to the maximum amount of displacement of a a
particle on the medium from its rest position. In a
sense, the amplitude is the distance from rest to
crest. Similarly, the amplitude can be measured from
the rest position to the trough position. In the diagram
above, the amplitude could be measured as the distance of
a line segment which is perpendicular to the rest
position and extends vertically upward from the rest
position to point A.
The wavelength
is another property of a wave which is portrayed in the
diagram above. The
wavelength of a wave
is simply the length of one complete wave cycle. If you
were to trace your finger across the wave in the diagram
above, you would notice that your finger repeats its
path. A wave has a repeating pattern. And the length of
one such repetition (known as a wave cylce) is the
wavelength. The wavelength can be measured as the
distance from crest to crest or from trough to trough. In
fact, the wavelength of a wave can be measured as the
distance from a point on a wave to the corresponding
point on the next cycle of the wave. In the diagram
above, the wavelength is the distance from A to E, or the
distance from B to G, or the distance from E to J, or the
distance from D to I, or the distance from C to H. Any
one of these distance measurements would suffice in
determining the wavelength of this wave.
A longitudinal
wave is a wave in which the particles of the medium
are displaced in a direction parallel to the direction of
energy transport. A longitudinal wave can be created in a
slinky if the slinky is stretched out horizontally and
the end coil is vibrated back-and-forth in a horizontal
direction. If a snap-shot of such a longitudinal wave
could be taken so as to freeze the shape of the
slinky in time, then it would look like the following
diagram.
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Because the coils of the slinky are
vibrating longitudinally, there are regions where they
become pressed together and other regions where they are
spread apart. A region where the coils are pressed
together in a small amount of space is known as a
compression. A
compression is a
point on a medium through which a longitudinal wave is
traveling which has the maximum density. A region where
the coils are spread apart, thus maximizing the distance
between coils, is known as a rarefaction. A
rarefaction is a
point on a medium through which a longitudinal wave is
traveling which has the minimum density. Points A, C and
E on the diagram above represent compressions and points
B, D, and F represent rarefactions. While a transverse
wave has an alternating pattern of crests and troughs, a
longitudinal wave has an alternating pattern of
compressions and rarefactions.
As discussed above, the wavelength
of a wave is the length of one complete cycle of a wave.
For a transverse wave, the wavelength is determined by
measuring from crest to crest. A longitudinal wave does
not have crest; so how can its wavelength be determined?
The wavelength can always be determined by measuring the
distance between any two corresponding points on adjacent
waves. In the case of a longitudinal wave, a wavelength
measurement is made by measuring the distance from a
compression to the next compression or from a rarefaction
to the next rarefaction. On the diagram above, the
distance from point A to point C or from point B to point
D would be representative of the wavelength.
Check
Your Understanding
Consider the diagram below in
order to answer questions #1-2.
1. The wavelength of the wave in the diagram above is
given by letter ______.
2. The amplitude of the wave in the diagram above is
given by letter _____.
3. Indicate the interval which represents one full
wavelength.
