1Phy107 Fall 061Exam Results• Exam:– Exam scoresposted onLearn@UW• No homeworkdue next weekD C BC B AB APhy107 Fall 062Today: waves• Have studied Newton’s laws, motion ofparticles, momentum, energy, etc.• Laws for describing 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!Phy107 Fall 063Wave Motion• A wave is a type of motion– But unlike motion of particles• A propagating disturbance– The rope stays in one place– The disturbance moves down the ropePhy107 Fall 064What 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.Phy107 Fall 065Motion 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.Phy107 Fall 066Energy transportTime=1.0 secTime=1.1 secZerovelocityZerovelocityPositive and negativevelocities• If rope section is not moving, kinetic energy is zero.• Determine motion by looking at rope position at twodifferent times.2Phy107 Fall 067How 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)2Phy107 Fall 068Waves 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.‘Crack’ occurs as tip breaks sound barrier!Phy107 Fall 069Wave 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 length! v =Fµ! velocity =elastic _ propertyinertial _ propertyPhy107 Fall 0610Waves 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 invertedPhy107 Fall 0611Superposition of 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 otherPhy107 Fall 0612Types of waves• Wave on a rope was a transverse wave• Transverse wave: each piece of the medium movesperpendicular to the wave propagation direction3Phy107 Fall 0613Longitudinal Waves• In a longitudinal wave, the elements ofthe medium undergo displacementsparallel to the motion of the wave• A longitudinal wave is also called acompression wavePhy107 Fall 0614Graph of longitudinal wave• A longitudinal wave can also berepresented as a graph• Compressions correspond to crests andstretches correspond to troughsPhy107 Fall 0615Sound waves• The medium transporting the wave is the air• The air is locally compressed, thencompresses air next to it, etc.• The sound velocity depends on– Mass density of the air (mass per unit volume)– and the ‘compressibility’ of the airPhy107 Fall 0616Producing a Sound Wave• Sound waves are longitudinal waves traveling through a medium• A tuning fork can be used as an example of producing a sound wave• As the tines vibrate, theydisturb the air near them• As the tine swings to theright, it forces the airmolecules near it closertogether• This produces a high densityarea in the air– Area of compression• Tine swings to left– Area of rarefactionPhy107 Fall 0617Sound from a Tuning Fork• As the tuning fork continues to vibrate, asuccession of compressions and rarefactionsspread out from the fork• A sinusoidal curve can be used to representthe longitudinal wave– Crests correspond to compressions and troughs torarefactionsPhy107 Fall 0618Continuous wave• Can generate a wave that occupies all of therope by continuing to shake the end up anddown.• This wave is present throughout the length ofthe rope, but also continually moves.• Can think of a wave source continuallyemitting waves along the string.• This is sort of like a string of pulses4Phy107 Fall 0619Waveform – A Picture of a Wave• Just like the pulse, acontinuous wave moves.• The red curve is a“snapshot” of the waveat some instant in time• The blue curve is later intime• A is a crest of the wave• B is a trough of the wavePhy107 Fall 0620Description of a Wave• Amplitude is themaximum displacementof string above theequilibrium position• Wavelength, λ, is thedistance between twosuccessive points thatbehave identicallyAmplitude• For instance, the distance between two crestsPhy107 Fall 0621Period, frequency and velocityof a wave• Period: time required to complete one cycle– Unit = seconds• Frequency = 1/Period= rate at which cycles are completed– Units are cycles/sec = Hertz• Period wavelength and velocity are related– If the wave travels one wavelength in the time ofone period then• velocity = wavelength/periodPhy107 Fall 0622Equation form• Velocity = Wavelength / Period• v = λ / T, or v = λf• f = Frequency = 1 / Period = 1/TPhy107 Fall 0623Periodic waves• Shake one end of a string up and down withperiod T (frequency f=1/T). The height (upor down) is the amplitude.• Peaks move at speed v so are separated bydistance (wavelength) λ=vT = v/f.• The wave can shake a fixed object with thatfrequency.Phy107 Fall 0624Examples• The speed of sound in air is 340 m/s.• A source period of 1 Hz=1/s produces awavelength of λ=v/f= 340 m• A string vibrating at frequency f= 340 Hzproduces a wavelength λ=v/f = 1 m5Phy107 Fall 0625Question• A sound wave is traveling through air when in encounters a largehelium-filled balloon. The sound velocity inside the balloon is greaterthan in the air. Compare the wavelength of the sound wave inside andoutside the balloon.A. λinside= λoutsideB. λinside> λoutsideC. λinside< λoutsideλ0λ1λ = v / fThe frequency inside theballoon is the same as outside.Use λ = v / f to find that thewavelength is
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