Chapter 21Chapter 21

Alternating Current Alternating Current Circuits Circuits

and Electromagnetic and Electromagnetic WavesWaves

AC CircuitAC Circuit

An AC circuit consists of a combination An AC circuit consists of a combination of circuit elements and an AC generator of circuit elements and an AC generator or sourceor source

The output of an AC generator is The output of an AC generator is sinusoidal and varies with time sinusoidal and varies with time according to the following equationaccording to the following equation Δv = ΔVΔv = ΔVmaxmax sin 2 sin 2ƒtƒt

Δv is the instantaneous voltageΔv is the instantaneous voltage ΔVΔVmaxmax is the maximum voltage of the generator is the maximum voltage of the generator ƒ is the frequency at which the voltage changes, ƒ is the frequency at which the voltage changes,

in Hzin Hz

Resistor in an AC CircuitResistor in an AC Circuit Consider a circuit Consider a circuit

consisting of an AC consisting of an AC source and a resistorsource and a resistor

The graph shows the The graph shows the current through and the current through and the voltage across the voltage across the resistorresistor

The current and the The current and the voltage reach their voltage reach their maximum values at the maximum values at the same timesame time

The current and the The current and the voltage are said to be voltage are said to be in in phasephase

More About Resistors in an More About Resistors in an AC CircuitAC Circuit

The direction of the current has no effect The direction of the current has no effect on the behavior of the resistoron the behavior of the resistor

The rate at which electrical energy is The rate at which electrical energy is dissipated in the circuit is given bydissipated in the circuit is given by P = iP = i22 R R

where i is the where i is the instantaneous currentinstantaneous current the heating effect produced by an AC current with a the heating effect produced by an AC current with a

maximum value of Imaximum value of Imaxmax is not the same as that of a is not the same as that of a DC current of the same valueDC current of the same value

The maximum current occurs for a small amount of The maximum current occurs for a small amount of timetime

rms Current and Voltagerms Current and Voltage

The The rms currentrms current is the direct is the direct current that would dissipate the current that would dissipate the same amount of energy in a same amount of energy in a resistor as is actually dissipated by resistor as is actually dissipated by the AC currentthe AC current

Alternating voltages can also be Alternating voltages can also be discussed in terms of rms valuesdiscussed in terms of rms values

maxmax

rms I707.02

II

maxmax

rms V707.02

VV

Ohm’s Law in an AC Ohm’s Law in an AC CircuitCircuit

rms values will be used when rms values will be used when discussing AC currents and voltagesdiscussing AC currents and voltages AC ammeters and voltmeters are AC ammeters and voltmeters are

designed to read rms valuesdesigned to read rms values Many of the equations will be in the Many of the equations will be in the

same form as in DC circuitssame form as in DC circuits Ohm’s Law for a resistor, R, in an Ohm’s Law for a resistor, R, in an

AC circuitAC circuit ΔVΔVrmsrms = I = Irmsrms R R

Also applies to the maximum values of v Also applies to the maximum values of v and iand i

Capacitors in an AC CircuitCapacitors in an AC Circuit

Consider a circuit containing a capacitor Consider a circuit containing a capacitor and an AC sourceand an AC source

The current starts out at a large value and The current starts out at a large value and charges the plates of the capacitorcharges the plates of the capacitor There is initially no resistance to hinder the flow There is initially no resistance to hinder the flow

of the current while the plates are not chargedof the current while the plates are not charged As the charge on the plates increases, the As the charge on the plates increases, the

voltage across the plates increases and the voltage across the plates increases and the current flowing in the circuit decreasescurrent flowing in the circuit decreases

More About Capacitors in More About Capacitors in an AC Circuitan AC Circuit

The current The current reverses directionreverses direction

The voltage across The voltage across the plates the plates decreases as the decreases as the plates lose the plates lose the charge they had charge they had accumulatedaccumulated

The voltage across The voltage across the capacitor lags the capacitor lags behind the current behind the current by 90°by 90°

Capacitive Reactance and Capacitive Reactance and Ohm’s LawOhm’s Law

The impeding effect of a capacitor on the The impeding effect of a capacitor on the current in an AC circuit is called the current in an AC circuit is called the capacitive reactancecapacitive reactance and is given by and is given by

When ƒ is in Hz and C is in F, XWhen ƒ is in Hz and C is in F, XCC will be in will be in ohmsohms

Ohm’s Law for a capacitor in an AC circuitOhm’s Law for a capacitor in an AC circuit ΔVΔVrmsrms = I = Irmsrms X XCC

Cƒ2

1XC

Inductors in an AC CircuitInductors in an AC Circuit

Consider an AC Consider an AC circuit with a source circuit with a source and an inductorand an inductor

The current in the The current in the circuit is impeded by circuit is impeded by the back emf of the the back emf of the inductorinductor

The voltage across The voltage across the inductor always the inductor always leads the current by leads the current by 90°90°

Inductive Reactance and Inductive Reactance and Ohm’s LawOhm’s Law

The effective resistance of a coil in The effective resistance of a coil in an AC circuit is called its an AC circuit is called its inductive inductive reactancereactance and is given by and is given by XXLL = 2 = 2ƒLƒL

When ƒ is in Hz and L is in H, XWhen ƒ is in Hz and L is in H, XLL will be in will be in ohmsohms

Ohm’s Law for the inductorOhm’s Law for the inductor ΔVΔVrmsrms = I = Irmsrms X XLL

The RLC Series CircuitThe RLC Series Circuit

The resistor, The resistor, inductor, and inductor, and capacitor can be capacitor can be combined in a combined in a circuitcircuit

The current in the The current in the circuit is the same circuit is the same at any time and at any time and varies sinusoidally varies sinusoidally with timewith time

Current and Voltage Current and Voltage Relationships in an RLC Relationships in an RLC CircuitCircuit

The instantaneous The instantaneous voltage across the voltage across the resistor is in phase resistor is in phase with the currentwith the current

The instantaneous The instantaneous voltage across the voltage across the inductor leads the inductor leads the current by 90°current by 90°

The instantaneous The instantaneous voltage across the voltage across the capacitor lags the capacitor lags the current by 90°current by 90°

Phasor DiagramsPhasor Diagrams

To account for the To account for the different phases of the different phases of the voltage drops, vector voltage drops, vector techniques are usedtechniques are used

Represent the voltage Represent the voltage across each element across each element as a rotating vector, as a rotating vector, called a called a phasorphasor

The diagram is called The diagram is called a a phasor diagramphasor diagram

Phasor Diagram for RLC Phasor Diagram for RLC Series CircuitSeries Circuit

The voltage across the The voltage across the resistor is on the +x resistor is on the +x axis since it is in phase axis since it is in phase with the currentwith the current

The voltage across the The voltage across the inductor is on the +y inductor is on the +y since it leads the since it leads the current by 90°current by 90°

The voltage across the The voltage across the capacitor is on the –y capacitor is on the –y axis since it lags axis since it lags behind the current by behind the current by 90°90°

Phasor Diagram, contPhasor Diagram, cont

The phasors are The phasors are added as vectors to added as vectors to account for the account for the phase differences in phase differences in the voltagesthe voltages

ΔVΔVLL and ΔV and ΔVCC are on are on the same line and the same line and so the net y so the net y component is ΔVcomponent is ΔVL L - - ΔVΔVCC

ΔVΔVmaxmax From the Phasor From the Phasor DiagramDiagram

The voltages are not in phase, so they The voltages are not in phase, so they cannot simply be added to get the cannot simply be added to get the voltage across the combination of the voltage across the combination of the elements or the voltage sourceelements or the voltage source

is the is the phase anglephase angle between the between the current and the maximum voltagecurrent and the maximum voltage

R

CL

2CL

2Rmax

V

VVtan

)VV(VV

Impedance of a CircuitImpedance of a Circuit

The impedance, The impedance, Z, can also be Z, can also be represented in a represented in a phasor diagramphasor diagram

R

XXtan

)XX(RZ

CL

2CL

2

Impedance and Ohm’s Impedance and Ohm’s LawLaw

Ohm’s Law can be applied to the Ohm’s Law can be applied to the impedanceimpedance ΔVΔVmaxmax = I = Imaxmax Z Z

Summary of Circuit Summary of Circuit Elements, Impedance and Elements, Impedance and Phase AnglesPhase Angles

Problem Solving for AC Problem Solving for AC CircuitsCircuits

Calculate as many unknown Calculate as many unknown quantities as possiblequantities as possible For example, find XFor example, find XLL and X and XCC

Be careful of units -- use F, H, Be careful of units -- use F, H, ΩΩ Apply Ohm’s Law to the portion of Apply Ohm’s Law to the portion of

the circuit that is of interestthe circuit that is of interest Determine all the unknowns asked Determine all the unknowns asked

for in the problemfor in the problem

Power in an AC CircuitPower in an AC Circuit

No power losses are associated with No power losses are associated with capacitors and pure inductors in an AC capacitors and pure inductors in an AC circuitcircuit In a capacitor, during one-half of a cycle In a capacitor, during one-half of a cycle

energy is stored and during the other half the energy is stored and during the other half the energy is returned to the circuitenergy is returned to the circuit

In an inductor, the source does work against In an inductor, the source does work against the back emf of the inductor and energy is the back emf of the inductor and energy is stored in the inductor, but when the current stored in the inductor, but when the current begins to decrease in the circuit, the energy is begins to decrease in the circuit, the energy is returned to the circuitreturned to the circuit

Power in an AC Circuit, Power in an AC Circuit, contcont

The average power delivered by The average power delivered by the generator is converted to the generator is converted to internal energy in the resistorinternal energy in the resistor PPavav = I = IrmsrmsΔVΔVRR = = IIrmsrmsΔVΔVrmsrms cos cos cos cos is called the is called the power factorpower factor of the of the

circuitcircuit Phase shifts can be used to Phase shifts can be used to

maximize power outputsmaximize power outputs

Resonance in an AC CircuitResonance in an AC Circuit

ResonanceResonance occurs at occurs at the frequency, ƒthe frequency, ƒoo, , where the current has where the current has its maximum valueits maximum value To achieve maximum To achieve maximum

current, the impedance current, the impedance must have a minimum must have a minimum valuevalue

This occurs when XThis occurs when XLL = = XXCC

LC2

1ƒo

Resonance, contResonance, cont Theoretically, if R = 0 the current would be Theoretically, if R = 0 the current would be

infinite at resonanceinfinite at resonance Real circuits always have some resistanceReal circuits always have some resistance

Tuning a radioTuning a radio A varying capacitor changes the resonance frequency A varying capacitor changes the resonance frequency

of the tuning circuit in your radio to match the station of the tuning circuit in your radio to match the station to be receivedto be received

Metal DetectorMetal Detector The portal is an inductor, and the frequency is set to a The portal is an inductor, and the frequency is set to a

condition with no metal presentcondition with no metal present When metal is present, it changes the effective When metal is present, it changes the effective

inductance, which changes the current which is inductance, which changes the current which is detected and an alarm soundsdetected and an alarm sounds

TransformersTransformers

An AC transformer An AC transformer consists of two consists of two coils of wire wound coils of wire wound around a core of around a core of soft ironsoft iron

The side The side connected to the connected to the input AC voltage input AC voltage source is called the source is called the primaryprimary and has N and has N11 turnsturns

Transformers, 2Transformers, 2

The other side, called the The other side, called the secondarysecondary, is connected to a , is connected to a resistor and has Nresistor and has N22

turnsturns The core is used to increase the The core is used to increase the

magnetic flux and to provide a magnetic flux and to provide a medium for the flux to pass from medium for the flux to pass from one coil to the otherone coil to the other

The rate of change of the flux is the The rate of change of the flux is the same for both coilssame for both coils

Transformers, 3Transformers, 3

The voltages are related byThe voltages are related by

When NWhen N22 > N > N11, the transformer is , the transformer is referred to as a referred to as a step upstep up transformer transformer

When NWhen N22 < N < N11, the transformer is , the transformer is referred to as a referred to as a step down step down transformertransformer

11

22 V

N

NV

Transformer, finalTransformer, final

The power input into the primary The power input into the primary equals the power output at the equals the power output at the secondarysecondary II11ΔVΔV11 = I = I22ΔVΔV22

You don’t get something for nothingYou don’t get something for nothing This assumes an ideal transformerThis assumes an ideal transformer

In real transformers, power efficiencies In real transformers, power efficiencies typically range from 90% to 99%typically range from 90% to 99%

Electrical Power Electrical Power TransmissionTransmission

When transmitting electric power over When transmitting electric power over long distances, it is most economical to long distances, it is most economical to use high voltage and low currentuse high voltage and low current Minimizes IMinimizes I22R power lossesR power losses

In practice, voltage is stepped up to In practice, voltage is stepped up to about 230 000 V at the generating about 230 000 V at the generating station and stepped down to 20 000 V station and stepped down to 20 000 V at the distribution station and finally to at the distribution station and finally to 120 V at the customer’s utility pole120 V at the customer’s utility pole

James Clerk MaxwellJames Clerk Maxwell Electricity and Electricity and

magnetism were magnetism were originally thought to originally thought to be unrelatedbe unrelated

in 1865, James Clerk in 1865, James Clerk Maxwell provided a Maxwell provided a mathematical theory mathematical theory that showed a close that showed a close relationship between relationship between all electric and all electric and magnetic magnetic phenomenaphenomena

Maxwell’s Starting PointsMaxwell’s Starting Points

Electric field lines originate on positive Electric field lines originate on positive charges and terminate on negative chargescharges and terminate on negative charges

Magnetic field lines always form closed loops Magnetic field lines always form closed loops – they do not begin or end anywhere– they do not begin or end anywhere

A varying magnetic field induces an emf and A varying magnetic field induces an emf and hence an electric field (Faraday’s Law)hence an electric field (Faraday’s Law)

Magnetic fields are generated by moving Magnetic fields are generated by moving charges or currents (Ampcharges or currents (Ampère’s Law)ère’s Law)

Maxwell’s PredictionsMaxwell’s Predictions Maxwell used these starting points and a Maxwell used these starting points and a

corresponding mathematical framework to corresponding mathematical framework to prove that prove that electric and magnetic fields play electric and magnetic fields play symmetric roles in naturesymmetric roles in nature

He hypothesized that a changing electric field He hypothesized that a changing electric field would produce a magnetic fieldwould produce a magnetic field

Maxwell calculated the speed of light to be Maxwell calculated the speed of light to be 3x103x1088 m/s m/s

He concluded that visible light and all other He concluded that visible light and all other electromagnetic waves consist of fluctuating electromagnetic waves consist of fluctuating electric and magnetic fields, with each varying electric and magnetic fields, with each varying field inducing the otherfield inducing the other

Hertz’s Confirmation of Hertz’s Confirmation of Maxwell’s PredictionsMaxwell’s Predictions

Heinrich Hertz Heinrich Hertz was the first to was the first to generate and generate and detect detect electromagnetic electromagnetic waves in a waves in a laboratory settinglaboratory setting

Hertz’s Basic LC CircuitHertz’s Basic LC Circuit When the switch is When the switch is

closed, oscillations closed, oscillations occur in the current occur in the current and in the charge on and in the charge on the capacitorthe capacitor

When the capacitor is When the capacitor is fully charged, the total fully charged, the total energy of the circuit is energy of the circuit is stored in the electric stored in the electric field of the capacitorfield of the capacitor At this time, the current At this time, the current

is zero and no energy is is zero and no energy is stored in the inductorstored in the inductor

LC Circuit, contLC Circuit, cont As the capacitor discharges, the energy stored As the capacitor discharges, the energy stored

in the electric field decreasesin the electric field decreases At the same time, the current increases and the At the same time, the current increases and the

energy stored in the magnetic field increasesenergy stored in the magnetic field increases When the capacitor is fully discharged, there is When the capacitor is fully discharged, there is

no energy stored in its electric fieldno energy stored in its electric field The current is at a maximum and all the energy The current is at a maximum and all the energy

is stored in the magnetic field in the inductoris stored in the magnetic field in the inductor The process repeats in the opposite directionThe process repeats in the opposite direction There is a continuous transfer of energy There is a continuous transfer of energy

between the inductor and the capacitorbetween the inductor and the capacitor

Hertz’s Experimental Hertz’s Experimental ApparatusApparatus

An induction coil is An induction coil is connected to two connected to two large spheres large spheres forming a capacitorforming a capacitor

Oscillations are Oscillations are initiated by short initiated by short voltage pulsesvoltage pulses

The inductor and The inductor and capacitor form the capacitor form the transmittertransmitter

Hertz’s ExperimentHertz’s Experiment

Several meters away from the Several meters away from the transmitter is the receivertransmitter is the receiver This consisted of a single loop of wire This consisted of a single loop of wire

connected to two spheresconnected to two spheres It had its own inductance and capacitanceIt had its own inductance and capacitance

When the resonance frequencies of the When the resonance frequencies of the transmitter and receiver matched, transmitter and receiver matched, energy transfer occurred between energy transfer occurred between themthem

Hertz’s ConclusionsHertz’s Conclusions

Hertz hypothesized the energy Hertz hypothesized the energy transfer was in the form of wavestransfer was in the form of waves These are now known to be These are now known to be

electromagnetic waveselectromagnetic waves Hertz confirmed Maxwell’s theory Hertz confirmed Maxwell’s theory

by showing the waves existed and by showing the waves existed and had all the properties of light waveshad all the properties of light waves They had different frequencies and They had different frequencies and

wavelengthswavelengths

Hertz’s Measure of the Hertz’s Measure of the Speed of the WavesSpeed of the Waves

Hertz measured the speed of the waves Hertz measured the speed of the waves from the transmitterfrom the transmitter He used the waves to form an interference He used the waves to form an interference

pattern and calculated the wavelengthpattern and calculated the wavelength From v = f From v = f λ, v was foundλ, v was found v was very close to 3 x 10v was very close to 3 x 1088 m/s, the known m/s, the known

speed of lightspeed of light This provided evidence in support of This provided evidence in support of

Maxwell’s theoryMaxwell’s theory

Electromagnetic Waves Electromagnetic Waves Produced by an AntennaProduced by an Antenna

When a charged particle undergoes an When a charged particle undergoes an acceleration, it must radiate energyacceleration, it must radiate energy If currents in an ac circuit change rapidly, If currents in an ac circuit change rapidly,

some energy is lost in the form of em wavessome energy is lost in the form of em waves EM waves are radiated by any circuit EM waves are radiated by any circuit

carrying alternating currentcarrying alternating current An alternating voltage applied to the An alternating voltage applied to the

wires of an antenna forces the electric wires of an antenna forces the electric charge in the antenna to oscillatecharge in the antenna to oscillate

EM Waves by an Antenna, EM Waves by an Antenna, contcont

Two rods are connected to an ac source, charges oscillate Two rods are connected to an ac source, charges oscillate between the rods (a)between the rods (a)

As oscillations continue, the rods become less charged, the As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = field near the charges decreases and the field produced at t = 0 moves away from the rod (b)0 moves away from the rod (b)

The charges and field reverse (c)The charges and field reverse (c) The oscillations continue (d)The oscillations continue (d)

EM Waves by an Antenna, EM Waves by an Antenna, finalfinal

Because the Because the oscillating charges oscillating charges in the rod produce in the rod produce a current, there is a current, there is also a magnetic also a magnetic field generatedfield generated

As the current As the current changes, the changes, the magnetic field magnetic field spreads out from spreads out from the antennathe antenna

Charges and Fields, Charges and Fields, SummarySummary

Stationary charges produce only Stationary charges produce only electric fieldselectric fields

Charges in uniform motion Charges in uniform motion (constant velocity) produce electric (constant velocity) produce electric and magnetic fieldsand magnetic fields

Charges that are accelerated Charges that are accelerated produce electric and magnetic produce electric and magnetic fields and electromagnetic wavesfields and electromagnetic waves

Electromagnetic Waves, Electromagnetic Waves, SummarySummary

A changing magnetic field A changing magnetic field produces an electric fieldproduces an electric field

A changing electric field produces A changing electric field produces a magnetic fielda magnetic field

These fields are These fields are in phasein phase At any point, both fields reach their At any point, both fields reach their

maximum value at the same timemaximum value at the same time

Electromagnetic Waves Electromagnetic Waves are Transverse Wavesare Transverse Waves

TheThe E E and and BB fields fields are perpendicular are perpendicular to each otherto each other

Both fields are Both fields are perpendicular to perpendicular to the direction of the direction of motionmotion Therefore, em Therefore, em

waves are waves are transverse wavestransverse waves

Properties of EM WavesProperties of EM Waves

Electromagnetic waves are transverse Electromagnetic waves are transverse waveswaves

Electromagnetic waves travel at the Electromagnetic waves travel at the speed of lightspeed of light

Because em waves travel at a speed that is Because em waves travel at a speed that is precisely the speed of light, precisely the speed of light, light is an light is an electromagnetic waveelectromagnetic wave

oo

1c

Properties of EM Waves, 2Properties of EM Waves, 2

The ratio of the electric field to the The ratio of the electric field to the magnetic field is equal to the speed of lightmagnetic field is equal to the speed of light

Electromagnetic waves carry energy as Electromagnetic waves carry energy as they travel through space, and this energy they travel through space, and this energy can be transferred to objects placed in can be transferred to objects placed in their paththeir path

B

Ec

Properties of EM Waves, 3Properties of EM Waves, 3

Energy carried by em waves is Energy carried by em waves is shared equally by the electric and shared equally by the electric and magnetic fieldsmagnetic fields

o

2max

o

2max

o

maxmax

2

Bc

c2

E

2

BE

areaunitperpowerAverage

Properties of EM Waves, Properties of EM Waves, finalfinal

Electromagnetic waves transport Electromagnetic waves transport linear momentum as well as energylinear momentum as well as energy For complete absorption of energy U, For complete absorption of energy U,

p=U/cp=U/c For complete reflection of energy U, For complete reflection of energy U,

p=(2U)/cp=(2U)/c Radiation pressures can be Radiation pressures can be

determined experimentallydetermined experimentally

Determining Radiation Determining Radiation PressurePressure

This is an apparatus This is an apparatus for measuring for measuring radiation pressureradiation pressure

In practice, the In practice, the system is contained system is contained in a vacuumin a vacuum

The pressure is The pressure is determined by the determined by the angle at which angle at which equilibrium occursequilibrium occurs

The Spectrum of EM The Spectrum of EM WavesWaves

Forms of electromagnetic waves Forms of electromagnetic waves exist that are distinguished by exist that are distinguished by their frequencies and wavelengthstheir frequencies and wavelengths c = ƒc = ƒλλ

Wavelengths for visible light range Wavelengths for visible light range from 400 nm to 700 nmfrom 400 nm to 700 nm

There is no sharp division between There is no sharp division between one kind of em wave and the nextone kind of em wave and the next

The EMThe EMSpectrumSpectrum

Note the overlap Note the overlap between types between types of wavesof waves

Visible light is a Visible light is a small portion of small portion of the spectrumthe spectrum

Types are Types are distinguished by distinguished by frequency or frequency or wavelengthwavelength

Notes on The EM Notes on The EM SpectrumSpectrum

Radio WavesRadio Waves Used in radio and television Used in radio and television

communication systemscommunication systems MicrowavesMicrowaves

Wavelengths from about 1 mm to 30 Wavelengths from about 1 mm to 30 cmcm

Well suited for radar systemsWell suited for radar systems Microwave ovens are an applicationMicrowave ovens are an application

Notes on the EM Notes on the EM Spectrum, 2Spectrum, 2

Infrared wavesInfrared waves Incorrectly called “heat waves”Incorrectly called “heat waves” Produced by hot objects and Produced by hot objects and

moleculesmolecules Readily absorbed by most materialsReadily absorbed by most materials

Visible lightVisible light Part of the spectrum detected by the Part of the spectrum detected by the

human eyehuman eye Most sensitive at about 560 nm Most sensitive at about 560 nm

(yellow-green)(yellow-green)

Notes on the EM Notes on the EM Spectrum, 3Spectrum, 3

Ultraviolet lightUltraviolet light Covers about 400 nm to 0.6 nmCovers about 400 nm to 0.6 nm Sun is an important source of uv lightSun is an important source of uv light Most uv light from the sun is absorbed in Most uv light from the sun is absorbed in

the stratosphere by ozonethe stratosphere by ozone X-raysX-rays

Most common source is acceleration of high-Most common source is acceleration of high-energy electrons striking a metal targetenergy electrons striking a metal target

Used as a diagnostic tool in medicineUsed as a diagnostic tool in medicine

Notes on the EM Notes on the EM Spectrum, finalSpectrum, final

Gamma raysGamma rays Emitted by radioactive nucleiEmitted by radioactive nuclei Highly penetrating and cause serious Highly penetrating and cause serious

damage when absorbed by living damage when absorbed by living tissuetissue

Looking at objects in different Looking at objects in different portions of the spectrum can portions of the spectrum can produce different informationproduce different information

Doppler Effect and EM Doppler Effect and EM WavesWaves

A Doppler Effect occurs for em waves, A Doppler Effect occurs for em waves, but differs from that of sound wavesbut differs from that of sound waves For sound waves, motion relative to a For sound waves, motion relative to a

medium is most importantmedium is most important For light waves, the medium plays no role since For light waves, the medium plays no role since

the light waves do not require a medium for the light waves do not require a medium for propagationpropagation

The speed of sound depends on its frame of The speed of sound depends on its frame of referencereference

The speed of em waves is the same in all The speed of em waves is the same in all coordinate systems that are at rest or moving with coordinate systems that are at rest or moving with a constant velocity with respect to each othera constant velocity with respect to each other

Doppler Equation for EM Doppler Equation for EM WavesWaves

The Doppler effect for em wavesThe Doppler effect for em waves

f’ is the observed frequencyf’ is the observed frequency f is the frequency emitted by the sourcef is the frequency emitted by the source u is the u is the relative speedrelative speed between the source between the source

and the observerand the observer The equation is valid only when u is much The equation is valid only when u is much

smaller than csmaller than c

c

u1f'f

Doppler Equation, contDoppler Equation, cont

The positive sign is used when the The positive sign is used when the object and source are moving object and source are moving towardtoward each othereach other

The negative sign is used when the The negative sign is used when the object and source are moving object and source are moving away fromaway from each othereach other

Astronomers refer to a Astronomers refer to a red shiftred shift when when objects are moving away from the earth objects are moving away from the earth since the wavelengths are shifted since the wavelengths are shifted toward the red end of the spectrumtoward the red end of the spectrum