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WavesWaves
Types, characteristics, Types, characteristics, propertiesproperties
Wave: definitionWave: definition
A quantity or disturbance that changes in A quantity or disturbance that changes in magnitude with respect to time at a given magnitude with respect to time at a given locationlocation
Also changes in magnitude from place to Also changes in magnitude from place to place at a given timeplace at a given time
Propagates through a medium or spacePropagates through a medium or space Transfers Transfers energyenergy, not matter, not matter water wave, sound, light, x-ray, water wave, sound, light, x-ray,
earthquakeearthquake
Wave Classification Wave Classification SchemesSchemes
Is medium needed Is medium needed for propagation?for propagation?
MechanicalMechanical ElectromagneticElectromagnetic
How do particles How do particles move compared to move compared to motion of motion of wavefront?wavefront?
TransverseTransverse LongitudinalLongitudinal
Mechanical WavesMechanical Waves
Require elastic medium for propagationRequire elastic medium for propagation Energy source vibrates particles of Energy source vibrates particles of
medium about an equilibrium positionmedium about an equilibrium position Each particle exerts force on adjacent Each particle exerts force on adjacent
particles passing energy alongparticles passing energy along Inertia of particles slows propagation of Inertia of particles slows propagation of
wave: wave speed depends on mediumwave: wave speed depends on medium
Mechanical WavesMechanical Waves
Particles move in SHM if wave train Particles move in SHM if wave train is generated by periodic motionis generated by periodic motion
Examples: water waves, sound Examples: water waves, sound waves, earthquake waves, vibrating waves, earthquake waves, vibrating stringsstrings
Electromagnetic WavesElectromagnetic Waves
Self-propagating--need no medium Self-propagating--need no medium for propagationfor propagation
Can travel through vacuum of spaceCan travel through vacuum of space Examples: light waves, microwaves, Examples: light waves, microwaves,
x-rays, radio & TV broadcastsx-rays, radio & TV broadcasts
Transverse WavesTransverse Waves
Displacement of particles is Displacement of particles is perpendicular to direction of wave perpendicular to direction of wave traveltravel
crestcrest: point of max. positive : point of max. positive displacementdisplacement
troughtrough: point of max. negative : point of max. negative displacementdisplacement
examples: water, light, string, all examples: water, light, string, all electromagnetic waveselectromagnetic waves
Longitudinal WavesLongitudinal Waves
Displacement of particles is parallel to Displacement of particles is parallel to direction of wave traveldirection of wave travel
Series of high and low pressure areas in Series of high and low pressure areas in mediummedium
CompressionCompression: high pressure area (like : high pressure area (like crest)crest)
RarefactionRarefaction: low pressure area (like : low pressure area (like trough)trough)
Ex: sound, Slinky, some earthquake wavesEx: sound, Slinky, some earthquake waves
Characteristics of All Characteristics of All WavesWaves
Energy: waves transport energyEnergy: waves transport energy Phase: relative position between wavesPhase: relative position between waves Frequency: how many waves per secondFrequency: how many waves per second Period: how long a time for one wavePeriod: how long a time for one wave Wavelength: distance between wavesWavelength: distance between waves Speed: how fast wave travelsSpeed: how fast wave travels Amplitude: how big the wave isAmplitude: how big the wave is
Wave EnergyWave Energy
Depends on amplitude, frequency, and Depends on amplitude, frequency, and density of mediumdensity of medium
Power (energy/time) is proportional to Power (energy/time) is proportional to square of amplitude and/or frequencysquare of amplitude and/or frequency
With no losses to system, each wave has With no losses to system, each wave has same energy as sourcesame energy as source
As wave moves outward, energy spreads As wave moves outward, energy spreads over larger area, reducing amplitudeover larger area, reducing amplitude
PhasePhase
In phase: waves (or particles) are In phase: waves (or particles) are moving together, peaks line up with moving together, peaks line up with peaks and troughs line up with troughspeaks and troughs line up with troughs
Out of phase: waves (or particles) are Out of phase: waves (or particles) are not aligned; totally out of phase, peaks not aligned; totally out of phase, peaks line up with troughs, troughs with line up with troughs, troughs with peakspeaks
Phase relationship can be expressed in Phase relationship can be expressed in degrees, related to circular motiondegrees, related to circular motion
FrequencyFrequency
number of wave pulses passing a number of wave pulses passing a point in a given timepoint in a given time
Measured from identical points on Measured from identical points on successive wavessuccessive waves
Symbol is Symbol is ff (or occasionally (or occasionally (nu))(nu)) Unit is hertz (Hz), has SI units of secUnit is hertz (Hz), has SI units of sec--
11
Old unit is cycles per secondOld unit is cycles per second
PeriodPeriod
Time for one wave cycleTime for one wave cycle Symbol is Symbol is TT Reciprocal of frequency Reciprocal of frequency T= 1/fT= 1/f
WavelengthWavelength
Distance between identical points on Distance between identical points on successive wavessuccessive waves
Also distance wave travels in one Also distance wave travels in one periodperiod
Measured in meters (or parts of Measured in meters (or parts of meters)meters)
Symbol is Symbol is (lambda) (lambda)
Wave SpeedWave Speed
Same as any speed: distance/time, symbolSame as any speed: distance/time, symbol vv, units m/s, units m/s
Depends on medium and often onDepends on medium and often on When speed depends onWhen speed depends on in medium, in medium,
medium is calledmedium is called dispersive dispersive CausesCauses dispersion dispersion, or spreading of wave , or spreading of wave
according to wavelength; ex: rainbowaccording to wavelength; ex: rainbow v =v = / T = f / T = f
AmplitudeAmplitude
In transverse wave, equals maximum In transverse wave, equals maximum displacement from equilibrium displacement from equilibrium positionposition
In longitudinal wave, equals In longitudinal wave, equals maximum pressure change from maximum pressure change from normal pressurenormal pressure
DampingDamping by dissipative forces by dissipative forces reduces amplitude as wave travelsreduces amplitude as wave travels
Wave PropertiesWave Properties
Rectilinear PropagationRectilinear Propagation Reflection Reflection ImpedanceImpedance RefractionRefraction DiffractionDiffraction InterferenceInterference
Rectilinear PropagationRectilinear Propagation
In uniform medium, waves travel in In uniform medium, waves travel in straight lines, perpendicular to straight lines, perpendicular to wavefrontwavefront
Wave velocity direction also Wave velocity direction also perpendicular to wavefrontperpendicular to wavefront
ReflectionReflection Occurs at boundary between two mediaOccurs at boundary between two media Wave is returned to original mediumWave is returned to original medium Can be partial or complete depending on Can be partial or complete depending on
how new media transmits wave energyhow new media transmits wave energy The more wave speed changes at media The more wave speed changes at media
boundary, the more wave is reflectedboundary, the more wave is reflected Law of reflection: angle of incidence Law of reflection: angle of incidence
equals angle of reflectionequals angle of reflection
Law of ReflectionLaw of Reflection
ImpedanceImpedance A measure of how easily a wave can A measure of how easily a wave can
be produced in a mediumbe produced in a medium Equals ratio of applied force Equals ratio of applied force
producing wave to resulting producing wave to resulting displacement velocitydisplacement velocity
If impedances of two media match, If impedances of two media match, wave is not reflected and is wave is not reflected and is transmitted with no losstransmitted with no loss
Impedance matching using Impedance matching using transformers important for energy transformers important for energy transmission systemstransmission systems
Impedance and Impedance and ReflectionReflection
If wave can’t create displacement in If wave can’t create displacement in particles of new media, impedance is particles of new media, impedance is infinite, wave is reflected out of infinite, wave is reflected out of phase: fixed end reflectionphase: fixed end reflection
If wave producing force can’t be If wave producing force can’t be transferred to new media, transferred to new media, impedance is zero and wave is impedance is zero and wave is reflected in phase: free end reflected in phase: free end reflectionreflection
RefractionRefraction Bending of wave path at boundary Bending of wave path at boundary
between mediabetween media Due to different wave speed in new Due to different wave speed in new
mediummedium Wave must strike boundary obliquelyWave must strike boundary obliquely Since Since v = fv = f , change in speed , change in speed
changes changes If If vv in new media < in new media < vv in old media, in old media,
wave bends towards normal of wave bends towards normal of boundary & vice versaboundary & vice versa
RefractionRefraction
Wave speed increasesWave speed increases
Refraction AppletRefraction Applet
DiffractionDiffraction
Spreading of wave beyond edges of Spreading of wave beyond edges of barrier or past small openingbarrier or past small opening
Causes bending of wavefrontCauses bending of wavefront Opening must be approximately Opening must be approximately
same size as wavelength to diffractsame size as wavelength to diffract Example: sound waves diffracted by Example: sound waves diffracted by
doorways, light waves aren’tdoorways, light waves aren’t
DiffractionDiffraction
Superposition PrincipleSuperposition Principle When two or more waves travel When two or more waves travel
through the same space (medium) at through the same space (medium) at the same time . . .the same time . . .
Each wave proceeds independently as Each wave proceeds independently as though no other waves were presentthough no other waves were present
The resultant displacement of any The resultant displacement of any particle is the vector sum of particle is the vector sum of displacements each wave would give displacements each wave would give it alone.it alone.
Produces complex waveforms Produces complex waveforms
InterferenceInterference
Effects due to two or more superposed Effects due to two or more superposed waves of similar frequencywaves of similar frequency
If 2 waves of same type and frequency If 2 waves of same type and frequency are in phase, displacements add, are in phase, displacements add, creating greater amplitude --creating greater amplitude -- constructive interferenceconstructive interference
Same waves out of phase, resultant Same waves out of phase, resultant displacement is now difference, displacement is now difference, decreasing amplitude --decreasing amplitude --destructive destructive interferenceinterference
Interference PatternsInterference Patterns Often destructive and constructive Often destructive and constructive
interference happens in different interference happens in different places at same time, creates places at same time, creates interference patterninterference pattern
Points of zero displacement, complete Points of zero displacement, complete cancellation are called cancellation are called nodesnodes
Points of max displacement called Points of max displacement called antinodesantinodes
Total wave energy doesn’t change, Total wave energy doesn’t change, just rearrangedjust rearranged
Standing WavesStanding Waves
Standing waveStanding wave: produced by : produced by interference of 2 periodic waves of interference of 2 periodic waves of same amplitude and wavelength same amplitude and wavelength traveling in opposite directionstraveling in opposite directions
Usually wave reflected onto itselfUsually wave reflected onto itself Nodes remain stationary, energy Nodes remain stationary, energy
remains standing at antinodesremains standing at antinodes Basis for all string and wind Basis for all string and wind
instrumentsinstruments