Waves

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Waves
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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.

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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.

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Transverse Wave Characteristics

• Crest .
• Trough .
• Amplitude (undisturbed position).

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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

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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

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Transverse vs. Longitudinal Waves
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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

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The Inverse RelationshipsT

• As the period , the .

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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

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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.

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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.

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Wave Interference
Interference Process by which two waves
meet producing a net amplitude.
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Wave Interference
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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.

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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 ( ).

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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.

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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.
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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.

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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.

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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 ?
?
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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 .

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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
  .