1Friday, Feb. 16 Phy107 Lecture 111Exam Results, HW4 reminder• Exam: Class average = 14.1/20 ( at B/BC boundary)– Exam scores posted this afternoon on Learn@UW– Exam solutions will be posted on course web page• HW3 (short) assigned at WileyPLUS - waves!– Due Tuesday, Feb. 20 midniteFriday, Feb. 16 Phy107 Lecture 11202468100 2 4 6 8 10 12 14 16 18 20PHYSICS 107 EXAM 1COUNTSCOREExam ResultsAverage at the B/BC boundaryAAAABABBBBCBCCCDDDFAverageFriday, Feb. 16 Phy107 Lecture 113Today: waves• Have talked about Newton’s laws, motion ofparticles, momentum, energy, etc.• Basically a description of things that move.• Waves are a different type of object– They move (propagate), but in a different way• Examples:– Waves on a rope– Sound waves– Water waves– Stadium wave!Friday, Feb. 16 Phy107 Lecture 114Wave Motion• A wave is a sort of motion– But unlike motion of particles• A propagating disturbance– The rope stays in one place– The disturbance moves down the ropeFriday, Feb. 16 Phy107 Lecture 115What is moving?• Mechanical waves require:– Some source of disturbance– A medium that can be disturbed– Some physical connection between or mechanismthough which adjacent portions of the mediuminfluence each other– Waves move at a velocity determined by the medium• The disturbance in the medium moves through themedium.• Energy moves down the rope.Friday, Feb. 16 Phy107 Lecture 116Motion of a piece of the rope• As the wave passes through, a piece of therope vibrates up and down.As the pulse passes, there is kinetic energyof motion.2Friday, Feb. 16 Phy107 Lecture 117Energy transport• Moving rope sections have some energy of motion (kinetic).• If rope section is not moving, kinetic energy is zero.• Determine motion by looking at rope position at two differenttimes.Time=1.0 secTime=1.1 secZerovelocityZerovelocityPositive and negativevelocitiesFriday, Feb. 16 Phy107 Lecture 118How does the wave travel• Energy is transmitted down the rope• Each little segment of rope at position xhas some mass m(x), and moves at a velocity v(x),and has kinetic energy! 12m(x)v(x)2Friday, Feb. 16 Phy107 Lecture 119QuestionKinetic energy (1/2)mass x (velocity)2is transported down rope as wave pulse moves.Suppose the rope gradually tapers along its length.The wave pulseA. speeds upB. slows downC. keeps same speedFriday, Feb. 16 Phy107 Lecture 1110Waves on a whipThe forward crack• The loop travels at velocity c, whereas amaterial point on top of the loop moves atvelocity 2c.Whip tapers from handle to tip, sothat wave velocity increases.Friday, Feb. 16 Phy107 Lecture 1111Wave on a whipNumerical solutions of a realistic whip(a) Initial loop(b) whip when the tip reaches the fastest velocity(c) whip at time t=0.02 s‘Crack’ occurs as tip breaks sound barrier!Friday, Feb. 16 Phy107 Lecture 1112Wave on a towel• Towel tip breaks soundbarrier on a good crack3Friday, Feb. 16 Phy107 Lecture 1113How does the pulse propagate?• Think of balls and springsFriday, Feb. 16 Phy107 Lecture 1114Wave speed• The speed of sound is higher in solids than in gases– The molecules in a solid interact more strongly,elastic property larger• The speed is slower in liquids than in solids– Liquids are softer, elastic property smaller• Speed of waves on a stringTensionMass per unit lengthFriday, Feb. 16 Phy107 Lecture 1115QuestionTwo ropes of different mass/length. On whichdoes the pulse propagate fastest?A. Heavier ropeB. Lighter ropeC. Both the sameFriday, Feb. 16 Phy107 Lecture 1116Waves can reflect• Whenever a traveling wavereaches a boundary, some orall of the wave is reflected• Like a particle, it bouncesback. But…• When it is reflected from afixed end, the wave is invertedFriday, Feb. 16 Phy107 Lecture 1117Magical waves• Two pulses are traveling inopposite directions• The net displacement whenthey overlap is the sum ofthe displacements of thepulses• Note that the pulses areunchanged after the passingthrough each otherFriday, Feb. 16 Phy107 Lecture 1118Wave summary1) Energy transfer along the direction ofpropagation.2) Speed is characteristic of the mediumelastic properties and inertia (mass) density3) obey the principle of superposition - twosuperposed disturbances add or subtract4Friday, Feb. 16 Phy107 Lecture 1119Types of waves• Wave on a rope was a transverse wave• Transverse wave: each piece of the medium movesperpendicular to the wave propagation directionFriday, Feb. 16 Phy107 Lecture 1120Longitudinal Waves• In a longitudinal wave, the elements ofthe medium undergo displacementsparallel to the motion of the wave• A longitudinal wave is also called acompression waveFriday, Feb. 16 Phy107 Lecture 1121Graph of longitudinal wave• A longitudinal wave can also berepresented as a graph• Compressions correspond to crests andstretches correspond to troughsFriday, Feb. 16 Phy107 Lecture 1122Question• Here is a sound wave.It is aA. Transverse waveB. Longitudinal waveC. Mixed longitudinal and transverseFriday, Feb. 16 Phy107 Lecture 1123Periodic waves• Many wavescontinuously repeat• Amplitude: maximumdisplacement of stringabove equilibrium• Wavelength, λ:distance between twosuccessive points thatbehave identicallyAmplitude• For instance, the distance between two crestsSnapshot in timeFriday, Feb. 16 Phy107 Lecture 1124Period and frequency of a wave• Period: time required to complete one cycle– Unit = seconds• Frequency = 1/Period= rate at which cycles are completed– Units are cycles/sec = Hertz5Friday, Feb. 16 Phy107 Lecture 1125Moving wave crests• Period = 1 second• Propagation speed = vFriday, Feb. 16 Phy107 Lecture 1126Same period, slower wave velocity• Period = 1 second• Propagation speed = v/2Friday, Feb. 16 Phy107 Lecture 1127Freq., wavelength, velocity are related• Period:– Time interval between crests at some location, or– Time for source to emit once cycle of the wave.• Wavelength:– Spatial distance between crests.• Source emits a crest once every period T.• This crest propagates at velocity v.• By the time the source emits another crest T secondslater, the first crest has moved vT.• So the distance between crests is vT.– This is the wavelength of the wave• Wavelength = velocity × periodFriday, Feb. 16 Phy107 Lecture 1128Equation form• Velocity = Wavelength / Period• v = λ / T, or v = λf• f = Frequency = 1 / Period = 1/TFriday, Feb. 16 Phy107 Lecture 1129Question• A sound
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