Waves
Types, characteristics, properties
Wave: definition
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A quantity or disturbance that changes in magnitude
with respect to time at a given location
Also changes in magnitude from place to place at a
given time
Propagates through a medium or space
Transfers energy, not matter
water wave, sound, light, x-ray, earthquake
Wave Classification Schemes
Is medium needed for
propagation?
 Mechanical
 Electromagnetic
How do particles move
compared to motion of
wavefront?
 Transverse
 Longitudinal
Mechanical Waves
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Require elastic medium for propagation
Energy source vibrates particles of medium
about an equilibrium position
Each particle exerts force on adjacent particles
passing energy along
Inertia of particles slows propagation of wave:
wave speed depends on medium
Mechanical Waves
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Particles move in SHM if wave train is generated
by periodic motion
Examples: water waves, sound waves,
earthquake waves, vibrating strings
Electromagnetic Waves
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Self-propagating--need no medium for
propagation
Can travel through vacuum of space
Examples: light waves, microwaves, x-rays, radio
& TV broadcasts
Transverse Waves
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Displacement of particles is perpendicular to
direction of wave travel
crest: point of max. positive displacement
trough: point of max. negative displacement
examples: water, light, string, all electromagnetic
waves
Longitudinal Waves
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Displacement of particles is parallel to direction of
wave travel
Series of high and low pressure areas in medium
Compression: high pressure area (like crest)
Rarefaction: low pressure area (like trough)
Ex: sound, Slinky, some earthquake waves
Characteristics of All Waves
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Energy: waves transport energy
Phase: relative position between waves
Frequency: how many waves per second
Period: how long a time for one wave
Wavelength: distance between waves
Speed: how fast wave travels
Amplitude: how big the wave is
Wave Energy
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Depends on amplitude, frequency, and density of
medium
Power (energy/time) is proportional to square of
amplitude and/or frequency
With no losses to system, each wave has same energy as
source
As wave moves outward, energy spreads over larger
area, reducing amplitude
Phase
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In phase: waves (or particles) are moving
together, peaks line up with peaks and troughs
line up with troughs
Out of phase: waves (or particles) are not
aligned; totally out of phase, peaks line up with
troughs, troughs with peaks
Phase relationship can be expressed in degrees,
related to circular motion
Frequency
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number of wave pulses passing a point in a
given time
Measured from identical points on successive
waves
Symbol is f (or occasionally n (nu))
Unit is hertz (Hz), has SI units of sec-1
Old unit is cycles per second
Period
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Time for one wave cycle
Symbol is T
Reciprocal of frequency T= 1/f
Wavelength
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Distance between identical points on successive
waves
Also distance wave travels in one period
Measured in meters (or parts of meters)
Symbol is l (lambda)
Wave Speed
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Same as any speed: distance/time, symbol v, units m/s
Depends on medium and often on l
When speed depends on l in medium, medium is
called dispersive
Causes dispersion, or spreading of wave according to
wavelength; ex: rainbow
v = l / T = fl
Amplitude
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In transverse wave, equals maximum
displacement from equilibrium position
In longitudinal wave, equals maximum pressure
change from normal pressure
Damping by dissipative forces reduces amplitude
as wave travels
Wave Properties
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Rectilinear Propagation
Reflection
Impedance
Refraction
Diffraction
Interference
Rectilinear Propagation
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In uniform medium, waves travel in straight
lines, perpendicular to wavefront
Wave velocity direction also perpendicular to
wavefront
Reflection
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Occurs at boundary between two media
Wave is returned to original medium
Can be partial or complete depending on how
new media transmits wave energy
The more wave speed changes at media
boundary, the more wave is reflected
Law of reflection: angle of incidence equals
angle of reflection
Law of Reflection
Impedance
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A measure of how easily a wave can be
produced in a medium
Equals ratio of applied force producing wave
to resulting displacement velocity
If impedances of two media match, wave is
not reflected and is transmitted with no loss
Impedance matching using transformers
important for energy transmission systems
Impedance and Reflection
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If wave can’t create displacement in particles of
new media, impedance is infinite, wave is
reflected out of phase: fixed end reflection
If wave producing force can’t be transferred to
new media, impedance is zero and wave is
reflected in phase: free end reflection
Refraction
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Bending of wave path at boundary between
media
Due to different wave speed in new medium
Wave must strike boundary obliquely
Since v = fl , change in speed changes l
If v in new media < v in old media, wave bends
towards normal of boundary & vice versa
Refraction
Wave speed increases
Refraction Applet
Diffraction
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Spreading of wave beyond edges of barrier or
past small opening
Causes bending of wavefront
Opening must be approximately same size as
wavelength to diffract
Example: sound waves diffracted by doorways,
light waves aren’t
Diffraction
Superposition Principle
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When two or more waves travel through the
same space (medium) at the same time . . .
Each wave proceeds independently as though
no other waves were present
The resultant displacement of any particle is
the vector sum of displacements each wave
would give it alone.
Produces complex waveforms
Interference
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Effects due to two or more superposed waves
of similar frequency
If 2 waves of same type and frequency are in
phase, displacements add, creating greater
amplitude -- constructive interference
Same waves out of phase, resultant
displacement is now difference, decreasing
amplitude --destructive interference
Interference Patterns
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Often destructive and constructive interference
happens in different places at same time, creates
interference pattern
Points of zero displacement, complete
cancellation are called nodes
Points of max displacement called antinodes
Total wave energy doesn’t change, just
rearranged
Standing Waves
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Standing wave: produced by interference of 2
periodic waves of same amplitude and
wavelength traveling in opposite directions
Usually wave reflected onto itself
Nodes remain stationary, energy remains
standing at antinodes
Basis for all string and wind instruments