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