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## Waves

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### Waves Definitions of Waves A wave is a traveling that carries through space and matter without transferring . Transverse Wave: A wave in which the disturbance ... – PowerPoint PPT presentation

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Title: Waves

1
Waves
2
Definitions of Waves
• A wave is a traveling that carries
through space and matter without transferring
.
• Transverse Wave A wave in which the disturbance
occurs to the direction of travel.
• A type of transverse wave is
• Longitudinal Wave A wave in which the
disturbance occurs to the direction of travel
of the wave.
• A type of longitudinal wave is
• Surface Wave A wave that has charact-eristics of
both and waves.

3
Types of Waves
• Mechanical Waves Require a such as ,
, of a spring or the fabric of a rope.
• Electromagnetic Waves can travel in the
absence of a medium.

4
Transverse Wave Characteristics
• Crest .
• Trough .
• Amplitude (undisturbed position).

John Wiley Sons
5
Transverse Wave Characteristics (cont.)
• Frequency(f) The number of the wave makes
in
• The unit for frequency is
• Wavelength(?) The minimum at which the
wave repeats the same pattern
• A single oscillation is also called a
• The units for wavelength are

6
Transverse Wave Characteristics (cont.)
• Velocity (v) of the wave
• Measured in
• The formula to calculate the speed of a wave is
• Period (T) it takes for the wave to complete
one
• The units for period is
• The formula to calculate the period is

7
Transverse vs. Longitudinal Waves
8
The Relationships v f?
• The of a wave is determined by the in
which it travels.
• That means that for a given medium
• and are inversely proportional.
• As one , the other

9
The Inverse RelationshipsT
• As the period , the .

10
Speed of a Wave on a String
• For a stretched rope or string
• Where
• Tension
• linear density
• As the tension , the speed .
• As the mass , the speed .
• This phenomena is commonly seen in

11
Waves at Boundaries
• A wave incident upon a fixed boundary will have
its reflected back in the opposite
direction. Note that the wave pulse is after
reflecting off the boundary.

www.electron4.phys.utk.edu
12
Interference
• occurs whenever two waves occupy the same
space at the same time.
• Law of When two or more waves are present
at the same time at the same place, the
disturbance is equal to the of the
disturbances from the individual waves.

13
Wave Interference
Interference Process by which two waves
meet producing a net amplitude.
www.electron4.phys.utk.edu
14
Wave Interference
15
Waves
• Wave An interference pattern resulting
from two waves moving in directions with the
same and such that they develop a
consistent repeating pattern of and
interference.

16
Waves
• Node The part of a standing wave where
interference is at all times ( o out of
phase).
• Antinode The part of the wave where interference
is maximized ( ).

17
Waves
• When a wave impacts a boundary, some of the
energy is , while some passes , or may be
.
• The wave that passes through is called a
wave.
• A wave that is transmitted through a boundary
will lose some of its energy.
• Electromagnetic radiation will both down and
have a wavelength when going into a denser
media.
• Sound will when transitioning into a denser
media.

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
The Wave Equation
• waves can be represented by the following
equation.
• y(x,t) ymsin(?t - ?x)
• Where
• ym
• ? (2?/?)
• x
• ? (2?f)
• t
• Note that the sum (?t - ?x) is in , not degrees.

20
The Wave Equation
• y(x,t) ymsin(?t - ?x)
• ? 2?/?
• Waveform
• repeats itself every .
• ? 2?f
• Waveform
• travels through 1
• (T) every .
• A phase constant (?) can be included in the phase
that represents all waves that do not pass
through the origin.

21
The Wave Equation An Alternate Representation
• y(x,t) ymsin(?t - ?x)
• Substituting for ? (2?f), ? (2?/?) and ym (A)
yields
• y(x,t) Asin2?(ft - x)
• or
• y(x,t) Asin2?(vt - x)

1 ?
?
22
Key Ideas
• Waves transfer without transferring .
• Longitudinal waves like that of sound require a
.
• Transverse waves such as electro-magnetic
radiation (light) do not require a .
• In transverse waves, displacement is to the
direction of the wave while in longitudinal
waves, the displacement is .

23
Key Ideas
• Waves can with one another resulting in
or interference.
• waves are a special case of constructive and
destructive interference for two waves moving in
opposite directions with the same , and
.