Waves
Periodic Motion
• We are surrounded by oscillations – motions that
repeat themselves
• Understanding periodic motion is essential for the
study of waves, sound, alternating electric currents,
light, etc.
– How many of you play an instrument?
• An object in periodic motion experiences restoring
forces that bring it back toward an equilibrium
position
• Those same forces cause the object to “overshoot”
the equilibrium position
• Think of a block oscillating on a spring or a
pendulum swinging back and forth past its
equilibrium position Demonstrate
Definitions of a Waves

A wave is a traveling disturbance that
carries energy through space and matter
without transferring mass.

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Transverse Wave: A wave in which the
disturbance occurs perpendicular to the
direction of travel (Light).
Longitudinal Wave: A wave in which the
disturbance occurs parallel to the line of travel
of the wave (Sound).
Surface Wave: A wave that has characteristics of both transverse and longitudinal
waves (Ocean Waves).
Wave types
How does a wave vary in position
and velocity?
-
Full body Demonstrate
- PVA graphs
Types of Waves
Mechanical Waves: Require a
material medium* such as air, water,
steel of a spring or the fabric of a
rope.
 Electromagnetic Waves: Light and
radio waves that can travel in the
absence of a medium.

*
Medium = the material through which the wave travels.
Wave Motion
• The wave is another basic model used to describe
the physical world (the particle is another example)
• Any wave is characterized as some sort of
“disturbance” that travels away from its source
• In many cases, waves are result of oscillations
– For example, sound waves produced by vibrating string
• For now, we will concentrate on mechanical waves
traveling through a material medium
– For example: water, sound, seismic waves
– The wave is the propagation of the disturbance: they do
not carry the medium with it
• Electromagnetic waves do not require a medium
• All waves carry momentum and energy
Types of Waves
• In solids, both transverse and longitudinal waves can
exist
– Transverse waves result from shear disturbance
– Longitudinal waves result from compressional disturbance
• Only longitudinal waves propagate in fluids (they can
be compressed but do not sustain shear stresses)
– Transverse waves can travel along surface of liquid,
though (due to gravity or surface tension)
• Sound waves are longitudinal
– Each small volume of air vibrates back and forth along
direction of travel of the wave
• Earthquakes generate both longitudinal (4–8 km/s P
waves) and transverse (2–5 km/s S waves) seismic
waves
– Also surface waves which have both components
Transverse Wave
Characteristics

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Crest: The high point of a wave.
Trough: The low point of a wave.
Amplitude: Maximum displacement from its
position of equilibrium (undisturbed position).
John Wiley & Sons
Transverse Wave
Characteristics (cont.)

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Frequency(f): The number of oscillations the
wave makes in one second
(Hertz = 1/seconds).
Wavelength(): The minimum distance at
which the wave repeats the same pattern
(= 1 cycle). Measured in meters.
Velocity (v): speed of the wave (m/s).
v = f

Period (T): Time it takes for the wave to
complete one cycle (seconds).
T = 1/f
The Inverse Relationships
v = f
The speed of a wave is determined by the
medium in which it travels.

Since velocity is constant for a given medium,
the frequency and wavelength must be
inversely proportional.
• As one increases, the other decreases
Frequency

Wavelength
The Inverse Relationships
T = 1/f
Similar to the inverse relationship
for frequency and wavelength, a
similar relationship exists for
frequency and the period.
Frequency

Period
Waves at Fixed Boundaries

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A wave incident upon a
fixed boundary will have
its energy reflected back
in the opposite direction.
Note that the wave pulse
is inverted after reflecting
off the boundary.
Example of Waves at
Fixed Boundaries
Start Per 5/6 here
www.electron4.phys.utk.edu
Interference

Interference occurs whenever two
waves occupy the same space at the
same time.

Law of Linear Superposition: When two or
more waves are present at the same time at
the same place, the resultant disturbance
is equal to the sum of the disturbances
from the individual waves.
Constructive Wave
Interference
Constructive Interference –
Process by which two waves
meet producing a net larger
amplitude.
www.electron4.phys.utk.edu
Destructive Wave Interference
Destructive Interference –
Process by which two waves
meet canceling out each other.
Standing Waves

Standing Wave: An interference pattern resulting
from two or more waves moving in opposite directions
with the same frequency and amplitude such that they
develop a consistent repeating pattern of constructive and
destructive interference.
 Node: The part of a standing wave where interference
is destructive at all times (180o out of phase) .
 Antinode: The part of the wave where interference is
maximized constructively.
 Standing Wave
Continuous Waves
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When a wave impacts a boundary, some of the
energy is reflected, while some passes through.
The wave that passes through is called a
transmitted wave.
A wave that is transmitted through a boundary
will lose some of its energy.
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Electromagnetic radiation will both slow down and have
a shorter wavelength when going into a denser media.
Sound will increase in speed when transitioning into a
denser media.
Speed of Light in different mediums
Continuous Waves – Higher
Speed to Lower Speed

Note the differences in wavelength and amplitude between
of the wave in the two different mediums
Transmitted Wave
v2
Displacement
Incident + Reflected Wave
-v1
v1
Boundary
Higher speed
Lower speed
Longer wavelength
Shorter wavelength
Note: This phenomena is seen with light traveling from air to water.
Waves at Boundaries
Examples of Waves at Boundaries
 Wave Types (Cutnell & Johnson)
 Waves - Colorado.edu
 Other Examples

Key Ideas

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Waves transfer energy without transferring
matter.
Longitudinal waves like that of sound require a
medium.
Transverse waves such as electro-magnetic
radiation do not require a medium.
In transverse waves, displacement is
perpendicular to the direction of the wave while
in longitudinal waves, the displacement is in the
same direction.
Key Ideas

Waves travel at different speeds in
different mediums.
Light slows down when going from air
to a liquid or solid.
 Sound speeds up when going from air
to a liquid or solid.


Waves can interfere with one
another resulting in constructive or
destructive interference.
Continuous Waves – Lower
Speed to Higher Speed
Note the differences in wavelength and amplitude between
of the wave in the two different mediums
Incident + Reflected Wave
Transmitted Wave
v2
-v1
v1
Displacement

Boundary
Lower speed
Higher speed
Shorter wavelength
Longer wavelength
Review of Springs
• Classic example of periodic motion:
– Spring exerts restoring force on block:
Fs  kx
(Hooke’s Law)
– k = spring constant (a measure of
spring stiffness)
– “Slinky” has k = 1 N/m; auto
suspensions have k = 105 N/m
– Movie of vertical spring:
1 2
• Elastic potential energy stored in spring: U el  kx
2
–
–
–
–
Uel = 0 when x = 0 (spring relaxed)
Uel is > 0 always
We do not have freedom to pick where x = 0
Uel conserves mechanical energy
Shock Absorbers
• Shock absorbers provide a
damping of the oscillations
– A piston moves through a viscous
fluid like oil
– The piston has holes in it, which
creates a (reduced) viscous force on the piston, regardless
of the direction it moves (up or down)
– Viscous force reduces amplitude of oscillations smoothly
after car hits bump in road
– When oil leaks out of the shock absorber, the damping is
insufficient to prevent oscillations
• Shock absorber is example of an
underdamped oscillator (see also
critically damped and overdamped)
Properties of Waves
• Superposition principle: The overlap of 2 or more
waves (having small amplitude) results in a wave
that is a point-by-point summation of each individual
wave
(constructive interference)
(destructive interference)
Properties of Waves
• Traveling waves can both reflect and transmit
across a boundary between 2 media
– Reflected wave pulse is inverted (not inverted) if wave
reaches a boundary that is fixed (free to move)