Physics 20: Waves
Teacher Notes
What is a Wave?
A wave is a disturbance that travels through a medium, transporting energy from
one location (its source) to another location.
A medium is any substance (such as air, water, or even a slinky) through which a
disturbance can travel.
Electromagnetic Waves versus Mechanical Waves
Electromagnetic Waves
Electromagnetic waves are disturbances that are made up of electrical and
magnetic fields. These waves do not require a medium. They travel through space
at approximately 3.00 x 108 m/s.
 E.g. Light, x-rays, and radio waves
Mechanical Waves
Mechanical waves are disturbances that require a medium to travel through.
 E.g. Slinky, water, and sound waves.
There are 3 types of mechanical waves - transverse, longitudinal, and surface.
Longitudinal versus Transverse Waves versus Surface Waves
One way to categorize waves is by comparing the direction the medium is traveling
in relation to the direction the waves are traveling.
1. Transverse Waves
A transverse wave is a wave in which particles of the medium move in a direction
perpendicular to the direction that the wave moves.
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Physics 20: Waves
Teacher Notes
2. Longitudinal Waves
A longitudinal wave is a wave in which particles of the medium move in a direction
parallel to the direction that the wave moves.
Waves traveling through a solid medium can be either transverse or longitudinal.
Yet waves traveling through the bulk of a fluid are always longitudinal waves.
While waves that travel within the depths of the ocean are longitudinal, the waves
that travel along the surface of the oceans are surface waves.
3. Surface Waves
A surface wave is a wave in which particles of the medium undergo a circular
motion.
In longitudinal and transverse waves, all the particles in the entire bulk of the
medium move in a parallel and a perpendicular direction (respectively) relative to
the direction of energy transport. In a surface wave, it is only the particles at the
surface of the medium that undergo the circular motion.
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Physics 20: Waves
Teacher Notes
Properties of a Wave
Anatomy of a Transverse Wave
If a snapshot of a transverse wave could be taken so as to freeze its shape 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. This is the position that the medium would assume if
there were no disturbance moving through it.
Points A, E and H on the diagram represent the crests of this wave. The crest of a
wave is the point on the medium that exhibits the maximum amount of positive or
upward displacement from the rest position.
Points C and J on the diagram represent the troughs of this wave. The trough of a
wave is the point on the medium that exhibits the maximum amount of negative or
downward displacement from the rest position.
The amplitude of a wave refers to the maximum amount of displacement of a
particle on the medium from its rest position. In a sense, the amplitude is the
distance from rest to crest (or rest to trough).
The wavelength of a wave is simply the distance of one complete wave cycle. The
wavelength can be measured as the distance from crest to crest or from trough to
trough.
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Physics 20: Waves
Teacher Notes
Anatomy of a Longitudinal Wave
If a snapshot of a longitudinal wave could be taken so as to freeze its shape in
time, then it would look like the following diagram.
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 that 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 that has the minimum density.
Points A, C and E on the diagram above represent compressions and points B, D, and
F represent rarefactions.
Speed of a Wave
To determine the speed of a wave, we use the Universal Wave Equation.
v = ƒλ
where
v = velocity (m/s)
ƒ = frequency (Hz which is 1/s)
λ = wavelength (m)
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Physics 20: Waves
Teacher Notes
The wave equation applies to all mechanical and electromagnetic waves - from
water waves to radio waves to x-rays.
Recall that the wavelength is the distance a wave travels in the time required for a
complete oscillation (crest to crest). The time for one oscillation is called the
period of the source. We know that:
.....
* It is important to note that the speed of a wave is a characteristic property of
the medium in which it travels. In other words, there is no way to change the
speed of a wave in a particular medium. *
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Physics 20: Waves
Teacher Notes
Wave Equation Examples
1. The wavelength of a water wave is .080 m. If the frequency of the wave
is 2.5 Hz (cycles per second), what is the velocity of the wave?
v = ƒl
v = (2.5 Hz)(.080m)
v = .20 m/s
The velocity is .20 m/s.
Notice the unit is m/s.
Remember that Hz is cycles/s. So, cycle/s X m gives cycle·m/s. We usually
disregard "cycle" from the unit, thus we end up with just m/s.
2. The distance between 2 crests is 4.0 m. The crests travel 9.0 m in 4.5 s.
Find the frequency of the waves.
First determine V.
Velocity is also determined by v = d/t.
distance traveled by crest is 9.0m
time is 4.5 s
Next find frequency using v = ƒλ.
The frequency of waves is 0.50 Hz.
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