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Title: Waves

1
Waves
2
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

3
Definitions of a Waves
• A wave is a traveling disturbance that carries
energy through space and matter without
transferring mass.
• 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 charact-eristics of
both transverse and longitudinal waves (Ocean
Waves).
• Wave types

4
How does a wave vary in position and velocity?
- Full body Demonstrate - PVA graphs
5
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.
6
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

7
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 (48 km/s
P waves) and transverse (25 km/s S waves)
seismic waves
• Also surface waves which have both components

8
Transverse Wave Characteristics
• 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
9
Transverse Wave Characteristics (cont.)
• 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

10
The Inverse Relationshipsv 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

11
The Inverse RelationshipsT 1/f
• Similar to the inverse relationship for frequency
and wavelength, a similar relationship exists for
frequency and the period.

12
Waves at Fixed Boundaries
• 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
13
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.

14
Constructive Wave Interference
www.electron4.phys.utk.edu
15
Destructive Wave Interference
16
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

17
Continuous Waves
• 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.
• 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

18
Continuous Waves Higher Speed to Lower Speed
• Note the differences in wavelength and amplitude
between of the wave in the two different mediums

Incident Reflected Wave
Transmitted Wave
Displacement
Lower speed Shorter wavelength
Higher speed Longer wavelength
Note This phenomena is seen with light traveling
from air to water.
19
Waves at Boundaries
• Examples of Waves at Boundaries
• Wave Types (Cutnell Johnson)
• Other Examples

20
Key Ideas
• 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.

21
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.

22
Continuous Waves Lower Speed to Higher Speed
• Note the differences in wavelength and amplitude
between of the wave in the two different mediums

23
Review of Springs
• Classic example of periodic motion
• Spring exerts restoring force on block
• 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
• Elastic potential energy stored in spring
• Uel 0 when x 0 (spring relaxed)
• Uel is gt 0 always
• We do not have freedom to pick where x 0
• Uel conserves mechanical energy

(Hookes Law)
24
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
critically damped and overdamped)

25
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)
26
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)