Ch16 sound and waves


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Ch16 sound and waves

  1. 1. Chapter 16Waves and Sound
  2. 2. SEMESTER 1: PHYSICSDate/weekLearning unitTheme/Topic Teaching MethodSEMESTER 11 -2Learning unit 1Dynamics of uniform circular motion ( Chapter 5) Lecture/ Question and answer/Whole Class Discussions3-4Learning unit 2 Waves and sound (Chapter 16)Lecture/ WCD/ CS/ Practical5-6Learning unit 3 Electromagnetic waves (Chapter 24)Lecture/ WCD/ CS/ Practical7Learning unit 4 Particles and waves (Chapter 29)Lecture/ WCD/ CS/ Practical8-9Learning unit 5 DC circuits (Chapter 20)Lecture/ WCD/ CS/ Practical10-11Learning unit 6 Magnetic Forces and Magnetic Fields (Chapter 21)Lecture/ WCD/ CS/ Practical12-13Learning unit 7 Electromagnetic Induction (Chapter 22)Lecture/ WCD/ CS/ PracticalMAY- JUNE EXAMINATIONS : PHYSICS
  3. 3. Sections to be covered• Section 16.1: The nature of waves• Section 16.2: Periodic waves• Section 16.3: The speed of a wave on a string• Section 16.4: Mathematical description of a wave• Section 16.5: The nature of sound• Section 16.6: The speed of sound• Section 16.9: The Doppler Effect
  4. 4. 16.1 The Nature of Waves1. A wave is a traveling disturbance.2. A wave carries energy from place to place.
  5. 5. 16.1 The Nature of Waveslongitudinal
  6. 6. 16.1 The Nature of WavesLongitudinal Wave
  7. 7. 16.1 The Nature of WavesWater waves are partially transverse and partially longitudinal.
  8. 8. 16.2 Periodic WavesPeriodic waves consist of cycles or patterns that are produced over andover again by the source.In the figures, every segment of the slinky vibrates in simple harmonicmotion, provided the end of the slinky is moved in simple harmonicmotion.
  9. 9. 16.2 Periodic WavesIn the drawing, one cycle is shaded in color.The amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.The wavelength is the horizontal length of one cycle of the wave.The period is the time required for one complete cycle.The frequency is related to the period and has units of Hz, or s-1.Tf1
  10. 10. 16.2 Periodic WavesfTv
  11. 11. 16.2 Periodic WavesExample 1 The Wavelengths of Radio WavesAM and FM radio waves are transverse waves consisting of electric andmagnetic field disturbances traveling at a speed of 3.00x108m/s. A stationbroadcasts AM radio waves whose frequency is 1230x103Hz and an FMradio wave whose frequency is 91.9x106Hz. Find the distance betweenadjacent crests in each wave.fTvfv
  12. 12. 16.2 Periodic WavesAM m244Hz101230sm1000.338fvFM m26.3Hz1091.9sm1000.368fv
  13. 13. 16.3 The Speed of a Wave on a StringThe speed at which the wave moves to the right depends on how quicklyone particle of the string is accelerated upward in response to the netpulling force.LmFvtensionlinear density
  14. 14. 16.3 The Speed of a Wave on a StringExample 2 Waves Traveling on Guitar StringsTransverse waves travel on each string of an electric guitar after thestring is plucked. The length of each string between its two fixed endsis 0.628 m, and the mass is 0.208 g for the highest pitched E string and3.32 g for the lowest pitched E string. Each string is under a tensionof 226 N. Find the speeds of the waves on the two strings.sm826m0.628kg100.208N2263-LmFvsm207m0.628kg103.32N2263-LmFvHigh ELow E
  15. 15. 16.3 The Speed of a Wave on a StringTo think aboutIs the speed of a transverse wave on a string the same as the speed atwhich a particle on the string moves?
  16. 16. 16.4 The Mathematical Description of a WaveWhat is the displacement y at time t of aparticle located at x?The quantity in brackets is called the phaseangle measured in radiansA particle located at a distance x also exhibits the SHM but with phase angle givenby
  17. 17. Your Turn
  18. 18. SolutionSOLUTION The dimensionless term 2 f t in Equation 16.4 corresponds to theterm 8.2 t in the given wave equation. The time t is measured in seconds (s), soin order for the quantity 8.2 t to be dimensionless, the units of the numericalfactor 8.2 must be s−1= Hz, and we have thatSimilarly, the dimensionless term 2 x/ in Equation 16.4 corresponds to the term0.54 x in the mathematical description of this wave. Because x is measured inmeters (m), the term 0.54 x is dimensionless if the numerical factor 0.54 hasunits of m−1. Thus,
  19. 19. Your TurnAnswer: 161 m/s
  20. 20. Tutorial exercises 26 02 2013
  21. 21. Tutorial Exercises 26 February 2013
  22. 22. 16.5 The Nature of Sound WavesLONGITUDINAL SOUND WAVES
  23. 23. 16.5 The Nature of Sound WavesThe distance between adjacent condensations is equal to thewavelength of the sound wave.
  24. 24. 16.5 The Nature of Sound WavesTHE FREQUENCY OF A SOUND WAVEThe frequency is the number of cyclesper second.A sound with a single frequency is calleda pure tone.The brain interprets the frequency in termsof the subjective quality called pitch.
  25. 25. 16.5 The Nature of Sound WavesTHE PRESSURE AMPLITUDE OF A SOUND WAVELoudness is an attribute ofa sound that depends primarilyon the pressure amplitudeof the wave.
  26. 26. 16.6 The Speed of SoundSound travels through gases,liquids, and solids at considerablydifferent speeds.
  27. 27. 16.6 The Speed of SoundIn a gas, it is only when molecules collide that the condensations andrarefactions of a sound wave can move from place to place.Ideal GasmkTv mkTvrms3KJ1038.1 23kgasesdiatomicidealfor57andgasesidealmonoatomicidealfor35Do Example 4: The physics of ultrasonic Ruler
  28. 28. 16.6 The Speed of SoundConceptual Example 5 Lightning, Thunder, and a Rule of ThumbThere is a rule of thumb for estimating how far away a thunderstorm is.After you see a flash of lighting, count off the seconds until the thunderis heard. Divide the number of seconds by five. The result gives theapproximate distance (in miles) to the thunderstorm. Why does thisrule work?
  29. 29. 16.6 The Speed of SoundLIQUIDS SOLID BARSadBvYvWhere B and Y are Bulk and Young’smodulus defined in section 10.7
  30. 30. 16.9 The Doppler EffectThe Doppler effect is thechange in frequency or pitchof the sound detected byan observer because the soundsource and the observer havedifferent velocities with respectto the medium of soundpropagation.
  31. 31. The Doppler effect is the apparent change infrequency and wavelength of a wave when theobserver and the source of the wave moverelative to each other.We experience the Doppler effect quite often in ourlives, without realizing that it is science takingplace.For example, the changing sound of a taxi hooteror ambulance as it drives past are the mostcommon examples.
  32. 32. 16.9 The Doppler EffectMOVING SOURCETvsssssofvfvvTvvvfvvffsso11
  33. 33. 16.9 The Doppler Effectvvffsso11source movingtoward a stationaryobserversource movingaway from a stationaryobservervvffsso11
  34. 34. 16.9 The Doppler EffectExample 10 The Sound of a Passing TrainA high-speed train is traveling at a speed of 44.7 m/s when the engineersounds the 415-Hz warning horn. The speed of sound is 343 m/s. Whatare the frequency and wavelength of the sound, as perceived by a personstanding at the crossing, when the train is (a) approaching and (b) leavingthe crossing?vvffsso11vvffsso11
  35. 35. 16.9 The Doppler EffectHz47711Hz415sm343sm7.44ofapproachingleavingHz36711Hz415sm343sm7.44of
  36. 36. 16.9 The Doppler EffectMOVING OBSERVERvvffvfvffossososo11
  37. 37. 16.9 The Doppler Effectvvff oso 1vvff oso 1Observer movingtowards stationarysourceObserver movingaway fromstationary source
  38. 38. 16.9 The Doppler Effectvvvvffsoso11GENERAL CASENumerator: plus sign applieswhen observer moves towardsthe sourceDenominator: minus sign applieswhen source moves towardsthe observer
  39. 39. 16.10 Applications of Sound in MedicineBy scanning ultrasonic waves across the body and detecting the echoesfrom various locations, it is possible to obtain an image.
  40. 40. 16.10 Applications of Sound in MedicineUltrasonic sound waves causethe tip of the probe to vibrate at23 kHz and shatter sections ofthe tumor that it touches.
  41. 41. 16.10 Applications of Sound in MedicineWhen the sound is reflectedfrom the red blood cells, itsfrequency is changed in akind of Doppler effect becausethe cells are moving.
  42. 42. Class Exercises 28 02 201376. A bird is flying directly toward a stationary bird-watcher and emits a frequency of 1500 Hz. Thebird-watcher, however, hears a frequency of 1560 Hz. What is the speed of the bird, expressed asa percentage of the speed of sound?REASONING:• The observer of the sound (the bird-watcher) is stationary, while the source (thebird) is moving toward the observer.• Therefore, the Doppler-shifted observed frequency is given by Equation 16.11.• This expression can be solved to give the ratio of the bird’s speed to the speed ofsound, from which the desired percentage follows directly.• The observed frequency fo is related to the frequency fs of the source, and theratio of the speed of the source vs to the speed of sound v by:Hence ,the ratio corresponds to 3.8 %
  43. 43. 77. From a vantage point very close to the track at a stock car race, you hear the sound emitted by amoving car. You detect a frequency that is 0.75 times as small as the frequency emitted by the carwhen it is stationary. The speed of sound is 343 m/s. What is the speed of the car?.REASONING :Since you detect a frequency that is smaller than that emitted by the car when the car is stationary, the car must bemoving away from you.Therefore, according to Equation 16.12, the frequency fo heard by a stationary observer from a source moving awayfrom the observer is given by:where fs is the frequency emitted from the source when it is stationary with respect to the observer, v is the speed ofsound, and vs is the speed of the moving source.This expression can be solved for vs .Solving for vs and noting thatWe get
  44. 44. 80. The security alarm on a parked car goes off and produces a frequency of 1000 Hz. The speed of sound is 343 m/s. Asyou drive toward this parked car, pass it, and drive away, you observe the frequency to change by 100 Hz. At what speedare you driving?REASONINGThe observed frequency changes because of the Doppler effect. As you drive toward the parked car (a stationarysource of sound), the Doppler effect is that given by Equation 16.13.As you drive away from the parked car, Equation 16.14 applies.o, toward s o o, away s oDriving toward parked car Driving away from parked car1 / and 1– /f f v v f f v v Subtracting the equation on the right from the one on the left gives the change in the observed frequencyo, toward o, away s o– 2 /f f f v vSolving for the observer’s speed (which is your speed), we obtain:o, toward o, awayos– 343 m/s 100 Hz17 m/s2 2 1000 Hzv f fvf
  45. 45. 78. Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring adolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimmingdirectly away at 10 m/s, the marine biologist measures the number of clicks occurring per second to beat a frequency of 2300 Hz. What is the difference (in Hz) between this frequency and the number ofclicks per second actually emitted by the dolphin?REASONING• The dolphin is the source of the clicks, and emits them at a frequency fs. The marine biologist measures a lower,Doppler-shifted click frequency fo, because the dolphin is swimming directly away.• The difference between the frequencies is the source frequency minus the observed frequency: fs − fo.• We will use the equation :o ss11f fvvwhere vs is the speed of the dolphin and v is the speed ofsound in seawater, to determine the difference between o 1vf fvSolving for fs we get:Therefore, the difference between the source and observed frequencies is:s ss o o o oso1 1 110.0 m/s2300 Hz 15 Hz1522 m/sv vf f f f fv vvfvTutorial Exercises Due on Monday: the 4th of March 2013Chapter 16: Problem number, 81, 82, 86 and 87 :
  46. 46. Chapter 24ElectromagneticWaves
  47. 47. What are electromagneticwaves• Electromagnetic waves consist of a combination ofoscillating electrical and magnetic fields, perpendicularto each other.This is difficult to visualize, however the waveform has similar characteristics ofother types of waves.
  48. 48. What are electromagneticwaves• Although they seem different, radio waves, microwaves,x-rays, and even visible light are all electromagneticwaves. They are part of the electromagnetic spectrum,and each has a different range of wavelengths, whichcause the waves to affect matter differently.• The creation and detection of the wave depend much onthe range of wavelengths.
  49. 49. Questions you may have include:• What is the electromagnetic spectrum?• What are the characteristics ofelectromagnetic waves?• How are these waves created anddetected?
  50. 50. Electromagnetic spectrum• The range of wavelengths for electromagnetic waves--from the very long tothe very short--is called the Electromagnetic Spectrum:
  51. 51. Electromagnetic Spectrum• Radio and TV waves are the longest usable waves, having a wavelength of1 mile (1.5 kilometer) or more.• Microwaves are used in telecommunication as well as for cooking food.• Infrared waves are barely visible. They are the deep red rays you get froma heat lamp.• Visible light waves are the radiation you can see with your eyes. Theirwavelengths are in the range of 1/1000 centimeter.• Ultraviolet rays are what give you sunburn and are used in "black lights"that make object glow.• X-rays go through the body and are used for medical purposes.• Gamma rays are dangerous rays coming from nuclear reactors and atomicbombs. They have the shortest wavelength in the electromagnetic spectrumof about 1/10,000,000 centimeter.
  52. 52. Properties• They do not need a medium for transmission. Otherwaves, such as sound waves, can not travel through avacuum. An electromagnetic wave is perfectly happy todo that.• Electromagnetic waves are transverse waves, similar towater waves in the ocean or the waves seen on a guitarstring.• The velocity of electromagnetic waves in a vacuum isapproximately 186,000 miles per second or 300,000kilometers per second, the same as the speed of light.When these waves pass through matter, they slow downslightly, according to their wavelength.
  53. 53. The speed of light• In 1865, Maxwell determined theoreticallythat electromagnetic waves propagatethrough a vacuum at a speed given by:
  54. 54. They all obey• Electromagnetic waves are split into different categories based ontheir frequency (or, equivalently, on their wavelength).• In other words, we split up the electromagnetic spectrum based onfrequency.• Visible light, for example, ranges from violet to red.• Violet light has a wavelength of 400 nm, and a frequency of 7.5 x1014 Hz.• Red light has a wavelength of 700 nm, and a frequency of 4.3 x 1014Hz.• Any electromagnetic wave with a frequency (or wavelength)between those extremes can be seen by humans.
  55. 55. Properties continued…• An electromagnetic wave, although itcarries no mass, does carry energy. It alsohas momentum, and can exert pressure(known as radiation pressure)• The energy carried by an electromagneticwave is proportional to the frequency ofthe wave.
  56. 56. 24.2 The Electromagnetic SpectrumThe Wavelength of Visible LightFind the range in wavelengths for visible light in the frequency rangebetween 4.0x1014Hz and 7.9x1014Hz.nm750m105.7Hz104.0sm1000.3 7148fcnm380m108.3Hz107.9sm1000.3 7148fc
  57. 57. Creating an electromagneticwave• From high school we already learned how moving charges (currents) produce magneticfields.• A constant current produces a constant magnetic field, while a changing current produces achanging field.• We can go the other way, and use a magnetic field to produce a current, as long as the magneticfield is changing.• This is what induced emf is all about. A steadily-changing magnetic field can induce a constantvoltage, while an oscillating magnetic field can induce an oscillating voltage.To Note:• an oscillating electric field generates an oscillating magnetic field• an oscillating magnetic field generates an oscillating electric field• What this means in practice is that the source has created oscillating electric andmagnetic fields, perpendicular to each other, that travel away from the source.• The E and B fields, along with being perpendicular to each other, are perpendicularto the direction the wave travels, meaning that an electromagnetic wave Theenergy of the wave is stored in the electric and magnetic fields
  58. 58. Energy in an electromagnetic wave• The energy in an electromagnetic wave is tied up in theelectric and magnetic fields.• In general, the energy per unit volume in an electric fieldis given by:And the magnetic energy density:In an electromagnetic wave propagating through a vacuum or air, the electric field and themagnetic field carry equal amounts of energy per unit volume of space.
  59. 59. 24.5 The Doppler Effect and Electromagnetic WavesElectromagnetic waves also can exhibit a Doppler effect, but itdiffers for two reasons:a) Sound waves require a medium, whereas electromagneticwaves do not.b) For sound, it is the motion relative to the medium that is important.For electromagnetic waves, only the relative motion of the sourceand observer is important.cvcvff so relrelif1
  60. 60. Sign Conventions for Relative MotionPlus Sign (source and observer cometogether)Minus sign (source and observer moveapart)1. The source is catching up with theobserver2. The observer is catching up with thesource3. The source and the observer movetoward one another1. The source is pulling away from theobserver2. The observer is pulling away from thesource3. The source and the observer bothmove away from one another
  61. 61. Focus on Concepts Problem 6The drawing shows four situations—A, B, C, and D—in which an observer and a sourceof electromagnetic waves can move along the same line. In each case the source emits awave of the same frequency, and in each case only the source or the observer is moving.The arrow in each situation denotes the velocity vector, which has the same magnitude ineach situation. When there is no arrow, the observer or thesource is stationary. Rank the frequencies of the observed electromagnetic waves indescending order (largest first) according to magnitude.(a) A and B (a tie), C and D (a tie)(b) C and D (a tie), A and B (a tie)(c) A and D (a tie), B and C (a tie)(d) B and D (a tie), A and C (a tie)(e) B and C (a tie), A and D (a tie)
  62. 62. Problem 1Theelapsedtimetis giveninhours,soitmustbeconvertedtoseconds:Thedistance,then,betweenearthandtheprobeis
  63. 63. Problem 5
  64. 64. Problem 92d(1)2d (1)Solving c f (Equation16.1)forfyields cf(2)
  65. 65. Problem 38Reasoning part:The observed frequency is given by:In situations A and B the observer and the source moveaway from each other, and the minus sign in Equation 24.6applies. In situation C the observer and the source movetoward each other, and the plus sign applies. Thus, theobserved frequency is largest in C.[Situation A, minus sign in Equation 24.6]
  66. 66. Calculation part[Situation A, minus sign in Equation 24.6]rel614 14relo s s 821.50 10 m/s1 1 4.57 10 Hz 1 4.55 10 Hz3.00 10 m/sv v v vv vf f fc c[Situation B, minus sign in Equation 24.6]rel614 14relo s s 82 33 1.50 10 m/s31 1 4.57 10 Hz 1 4.50 10 Hz3.00 10 m/sv v v vv vf f fc c[Situation C, plus sign in Equation 24.6]rel614 14relo s s 822 1.50 10 m/s21 1 4.57 10 Hz 1 4.62 10 Hz3.00 10 m/sv v v vv vf f fc c
  67. 67. 24.5 The Doppler Effect and Electromagnetic WavesYour Chance: Study Example: Radar Guns and Speed TrapsPolice use radar guns and the Doppler effect to catch speeders.A moving car approaches a stationary police car. A radar gun emits anelectromagnetic waves that reflects form the oncoming car. The reflectedWave returns to the police car with a frequency measured by on-boardequipment that is different from the emitted frequency. One such radaremits a wave whose frequency is 8.0x109Hz. When the speed is 39m/sand the approach is essentially head on, what is the difference betweenthe frequency of the wave returning to the police car and that emittedby the radar gun.
  68. 68. 24.5 The Doppler Effect and Electromagnetic Waves1 relcvff so1 relcvff oofrequency “observed”by speeding carfrequency observedby police carsoso fcvfff rel1cvfff ssorel2ss fcvcvf relrel11ss fcvf rel21cvcvfsrelrel2cvrel2
  69. 69. C Y U 7 page 24.5• An astronomer measures a Doppler change in frequency for light reachingthe earth from a distant star, from this measurement, can the astronomertell whether the star is moving away from the earth or the earth movingaway from the star?• Answer: No The same Doppler change results when the star moves awayfrom the earth and when the earth moves away from the star