Waves

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• Waves

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Waves

• A propagation of energy through a medium without
  a transfer of the medium.

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Two Types of Waves

• 1) Transverse Wave a wave where the disturbance
  of the medium is perpendicular to the direction
  of energy motion.
• Transverse Wave Diagram
• Transverse Diagram 1
• Transverse Water Wave
• Transverse Wave Animation
• Transverse Wave Animation 1
• Longitudinal Wave (Compression Wave) a wave
  where the disturbance of the medium is parallel
  to the direction of energy motion.
• Sound is a longitudinal wave.
• Longitudinal Wave 1
• Longitudinal Wave 2
• Longitudinal Wave 3
• Longitudinal Wave Animation
• Compression a region of high density in a
  longitudinal wave
• Rarefaction a region of low density in a
  longitudinal wave

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Components of a Transverse Wave
wavelength (?)
crest
amplitude
Equilibrium Position
trough

• Crest the location of maximum displacement on a
  wave.
• Trough the location of the lowest displacement
  on a wave.
• Equilibrium position the undisturbed position
  of the medium
• Amplitude the displacement from the equilibrium
  position to crest or trough.
• The amplitude represents the energy in a
  wave.
• Wavelength (?) the distance between the same
  two locations on adjacent waves.

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Wave Pulse

• A single disturbance in the medium
• Wave Pulse Animation
• Wave Pulse

Periodic Wave

• A repetitious wave.
• Transverse Wave

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Two categories of waves

• Matter Wave (Mechanical Wave) a wave that needs
  a medium to travel through
• Examples Earthquake The Earthquake Shake
• A vibrating guitar
  string
• The surface of water Water
  Surface Wave
• Electromagnetic Wave a wave that does not need
  a medium to travel through
• Example Radio waves, TV waves, light,
  x-rays Electromagnetic Waves

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Speed of a Wave
wavelength (?)
T period the amount of time for one wave to be
created.

• f frequency the number of waves created in one
  second.
• Frequency is measured in Hertz (Hz) which has the
  fundamental unit of s-1 (1/s)

T1/f
vd/t ? /T
v? / T
vf?

• Example What is the speed of the wave above if
  its created in 4.0 s
• and has a wavelength of 12.0 m?

v?/T 12.0 m / 4.0s 3.0 m/s
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Speed of a wave (cont.)
?
d
vd/t
f waves / time
vf?
The above waves are created in 6.0 s and has a
wavelength of 9.0 m. What is the speed of the
waves?
f3 waves/6.0s .50 Hz
vf?(.50 Hz)(9.0m)4.5 m/s
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Wave Properties
In one medium

• Speed Unchanged as it travels through a medium.
  The wave speed is dependent only on the
  properties of the medium.
• Frequency Increased Wavelength Decreases

• Frequency Decreased Wavelength Increases

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A graphical explanation of why wavelength is
dependent on speed
The speed of the vehicle are constant.
A larger frequency of cars
A smaller frequency of cars
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Mathematical explanation of why wavelength varies
with speed
Speed remains constant in a medium.
v
f

?
f
Large frequency, short wavelength
v

?
?
Small frequency, long wavelength
v

f
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Wave Properties between Media
Wave Reflection
Incident wave
transmitted wave
reflected wave
Medium 2
Medium 1
Incident wave The original wave that approaches
the boundary between two media. Reflected wave
The portion of the wave redirected back into the
first medium. Transmitted wave The portion of
the original wave that the transferred into the
new medium.
The more similar the properties between the two
media the more of the wave that is transmitted.
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Phase of the Reflected Wave
phase the position of a wave.
inverted wave (180º phase shift)
erect wave (0º phase shift)
incident wave
incident wave
incident wave
reflected wave
reflected wave
Reflected wave is erect
Reflected wave is inverted
If the new medium is more dense than the previous
medium, the reflected wave will be inverted.
If the new medium is less dense than the previous
medium, the reflected wave will be erect.
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Wave Interference

• Interference- The interaction between two or more
  waves simultaneously occupying the same location.
• Principle of superposition the algebraic sum of
  two or more waves.

Constructive interference will occur in the
following situation when the waves occupy the
same position at the same time.
B
A
The principle of superposition shows the
resulting wave of both Interfering.
Constructive interference
AB
A
B
The wave continue traveling in the same
direction unaffected by the wave interference.
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Destructive interference will occur in the
following situation when the waves occupy the
same position at the same time.
A
B
The principle of superposition shows the
resulting wave of both Interfering.
Destructive interference
AB
After the interference the waves continue
traveling In the same direction unaffected by
the interference.
A
B
Total Destructive interference will occur when
two waves with equal magnitude, but opposite
directions interfere as show below.
A
B
AB
The waves continue traveling in the same
direction unaffected by the wave interference.
A
B
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Wave Component Properties Traveling between Media
Amplitude Decreases Wavelength
Changes Speed Changes Frequency
Constant
End
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Wave Phenomena
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Standing Waves
Fluctuating stationary waves formed by the
interference of traveling waves of the same
frequency, speed and amplitude moving in
opposite directions.
Standing wave demonstration
Standing Wave Diagram
Standing Wave Animation
Standing Wave Animation 1
Standing Wave Animation 2
Standing Wave Animation 3
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Wave Fronts
wave front a short hand notation of
representing the crest of a wave.
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Law of Reflection
The angle of incidence is equal to the angle of
reflection. (?i?r)
Incident wave
Barrier
?i
?r
Normal a perpendicular to the surface of an
object.
?iangle of incidence
Reflected wave
?rangle of reflection
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Refraction

• The change in direction of a wave when traveling
  from one medium to another.

medium 2
medium 1
wave direction in medium 2
wave direction in medium 1
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Diffraction

• Diffraction the bending and spreading of a
  wave that passes through an opening
• or around an obstacle.
• The smaller the opening compared the wavelength
  of the wave, the greater the
• diffraction.

Diffraction
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Sound
The vibration of air molecules in a medium
perceivable by the human ear.
Pitch how the frequencies of sound is perceived.

• Audible frequency range 20 Hz to 20 kHz
• Infrasonic region Frequencies less than 20 Hz
• Ultrasonic region Frequencies above 20 kHz
• The ultrasonic region limit is 1 GHz.

• Sound in air is a longitudinal wave.
• Sound in a liquid or gas is primarily
  longitudinal, but contains a small fraction of a
• traverse wave component.

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Speed of Sound

• The speed of sound in air at 0ºC is 331 m/s.
• The speed of sound increases as temperature
  increases.
• v(331m/s .6Tc) for environmental temperatures.
• v331m/s(1Tc/273m/s)1/2 for higher temperatures.

Mach number A multiple of the speed of sound
Example Mach 2 at 0ºC is 662 m/s.
993 m/s
What is the speed of a jet traveling at Mach 3 at
0º?
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The Doppler Effect

• The perceived frequency change of sound because
  of a wavelength change due to relative motion
  between a source and an observer.

numerator source moving towards observer
- source moving away from observer
denominator - observer moving towards source
observer moving away from source
v speed of sound at a given temperature vo
speed of the observer of the sound vs speed of
the source of the sound
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Resonance

• A matched frequency between a source and an
  object which causes increased oscillation
  vibrations of the object.

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Beats

• Fluctuations in intensity between two sound
  frequencies due constructive and destructive
  interference of the sound waves.
• fbf1-f2
• fbbeat frequency