Hey it's professor Dave, let's learn about waves.
We have already examined one kind of vibration when
we looked at springs and Hookes law and the
periodic motion that results. Now let's
look at another type of vibration that
can also result in periodic motion: waves.
These should be quite familiar if you've
ever been to the beach, but those aren't
the only kinds of waves. Light and sound
can both be considered waves as well, so
we will need to learn about the
properties of waves. Waves always
originate with some event or disturbance
like a pebble falling into a pond, and
this disturbance will then propagate
outwards from this point. In this way, we
can consider any wave to be a kind of
traveling disturbance that carries
energy from place to place. Apart from
the radial waves on the pond, waves can
also be strictly linear, like if you
shake a taut rope. In both cases the wave
is traveling through a material medium
so they are called mechanical waves.
Mechanical waves can be transverse waves
where the disturbance is perpendicular
to the direction the wave is traveling
or longitudinal waves, where the
disturbance is parallel to the direction
the wave is traveling, either by
compression or rarefaction.
With mechanical waves, the medium does not
travel with the wave, just the energy is
carried by the wave, so in the ocean the
wave will travel a great distance, but
any individual water molecule won't go
too far, it is only energy that travels
along with the wave. The same can be said
for people doing the wave at a stadium.
The wave travels, but all of the people
stay in their own seats. However, not all
waves are mechanical waves, some do not
require a medium to travel through, like
any kind of electromagnetic wave, which
we know of as light. These waves can
travel through the vacuum of space, which
is why we are able to see celestial
objects in the night sky.
A wave whose source is a vibration with
simple harmonic motion will be a sine
wave, because the periodic motion of the
wave produces a graph of the
trigonometric function y = sin x
We need to label a few details with sine
waves. First there is the amplitude of
the wave. For a transverse wave like this
the amplitude is the displacement of the
wave in the direction perpendicular to
the direction of its motion, or the
distance from the middle to a crest or
trough. The greater the amplitude, the
more energy the wave carries with it
which is why you shouldn't try to surf
30-foot waves unless you are an expert.
In addition, each wave will carry a
wavelength, represented by the Greek
letter lambda. This is the length of one
cycle of the wave, which is easily
measured from one crest to the next.
The time required to complete one cycle is
called the period. There will also be a
frequency, which is the number of
wavelengths that pass by a particular
spot per unit time, represented by the
Greek letter nu. Frequency will
typically be measured in Hertz, which are
inverse seconds, meaning the number of
waves that occur per second. We will
learn all kinds of math associated with
graphing these sine curves in the
upcoming mathematics course. For now we
can just stick to a qualitative
discussion. Sound is also brought to our
ears through waves, though these are
longitudinal waves. A sound initiates
with a vibration, like a plucked string.
This vibration requires a medium in
which to travel, like a solid, liquid, or
gas. Sound can't travel in a vacuum, which
is why there is no sound in space
despite what you hear in movies.
Typically, sound travels through the air
causing vibrations in atmospheric
molecules as it passes, just like a wave
in the ocean does to water molecules.
Each sound wave will carry a frequency
that is equal to the frequency
of the vibration that initiated it.
The speed at which the wave will travel is
equal to the wavelength times the
frequency, and mechanical waves will
travel at a constant speed for any given
medium, though that speed is different
depending on the particular medium.
Interestingly, sound travels four times
faster in water than air, and 17 times
faster through steel than air, but when
we refer to the speed of sound we
typically mean as it moves through the
atmosphere, which will be constant, since
a greater frequency will be accompanied
by a smaller wavelength. Let's check comprehension.
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