Periodic Motion Motion that repeats in a regular cycle is called periodic motion The revolution of a planet about its sun is an example of periodic motion The highly reproducible period T of a planet is also called its year ID: 1022638
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1. Vibrations & WavesVibrations and Waves
2. Periodic MotionMotion that repeats in a regular cycle is called periodic motion. The revolution of a planet about its sun is an example of periodic motion. The highly reproducible period (T) of a planet is also called its year.Mechanical devices on earth can be designed to have periodic motion. These devices are useful timers. They are called oscillators.
3. Periodic MotionMotion that repeats in a regular cycle is called periodic motion or simple harmonic motion. Pendulum - Mass on a spring
4. Simple Pendulum Simple harmonic motion can be demonstrated by the swing of a pendulum. A simple pendulum consists of a massive object, called the bob, suspended by a string or light rod of length L.http://www.science-animations.com/support-files/energy.swf http://www.wiley.com/college/halliday/0470469080/simulations/fig08_07/fig08_07.html
5. Forces on PendulumqLxAt the left and right positions, the net force and acceleration are maximum, and the velocity is zero. At the middle position in the figure, the net force and acceleration are zero, and the velocity is maximum
6. SHM - PendulumqLxYou can see that the net force is a restoring force; that is, it is opposite the direction of the displacement of the bob and is trying to restore the bob to its equilibrium position.
7. GPE maxGPE maxGPE zeroKE 0KE maxKE 0Fnet and a maxFnet and a zeroFnet and a maxv zerov maxv zerohttp://www.science-animations.com/support-files/energy.swf Pendulum
8. Simple Harmonic MotionRequres a RESTORING FORCE - force that restores object to its equilibrium position that is directly proportional to the displacement of the objectPeriod (T): time it takes the object to complete one cycle of motion. Units - secondsFrequency (f): number of cycles in one second. Units - seconds-1 or HertzAmplitude (A) : maximum distance that the object moves from the equilibrium positionUnits - meters
9. Experimentally determine what T depends on before derive an expression
10.
11. Experimental DesignPurpose?Determine relationship between two different variablesControlled ExperimentsManipulate only one variable in an experimentObserve its effect on a second variableHold ALL other variables in the experiment CONSTANT
12. Variables Any factor that might affect the behavior of an experiment. Independent VariablesFactor that is changed or manipulated during the experiments Always plotted on the x-axisTime is usually the independent variableDependent VariablesFactor that depends on the independent variableAlways plotted on the y-axis
13. Collecting and Recording Data At least 6 data points are necessary for a good graph.Independent variable should cover a range of at least 10 fold if possible (eg. 0.2 to 2.0 m)Raw data is recorded in a data table immediately as it is collected in the lab.Data TableConstruct data table before collecting the dataIndependent variable in leftmost column of data tableEvery column is labeled with the variable name being measured AND the units in parenthesesValues in table do not have units.Same number of decimal places in each column
14. Graphing Data Purpose Determine relationship between two variablesPlot data as scatter graphs (do not connect the data points)GraphsAlways include Title (in WORDS)DEPENDENT vs. INDEPENDENT variable Label each axis with the variable and the UNITSRecognize common relationships in graphsConnect the data points with a line or curve of best fit to show the relationship between variables
15. Graphing Data Force Applied vs. MassDirect RelationshipTitle(words)Axes labeled with variable symbols (not words) and unitsF=2mDependent variableIndependent variable
16. Simple Harmonic Motion for a Pendulum independent of mass independent of amplitude Dependent on g (gravitational strength)
17. Example ProblemOn a planet with an unknown value of g, the period of a 0.75 m long pendulum is 1.8 sec. What is g for this planet?
18. ResonanceResonance is a special form of simple harmonic motion in which the additions of small amounts of force at specific times in the motion of an object cause a larger and larger displacement.Resonance from wind, combined with the design of the bridge supports, may have caused the original Tacoma Narrows Bridge to collapse.London Millenium bridge Tacoma Narrows Bridge Tacoma Narrows Bridge2 https://www.youtube.com/watch?v=JiM6AtNLXX4 glass shattering montage
19. Waves Disturbance that travels through a medium from one location to another location.
20. WavesDisturbance that carries energy through matter and space. A wave transports energy NOT matterWaves travel through matter or spaceNewton’s laws of motion & conservation of energy govern the motion of waves
21. Mechanical WavesMechanical waves require a medium to travel through Water AirRopes Travel through the medium, but do not carry the medium awayElectromagnetic WavesElectromagnetic waves do NOT require a medium to travel through
22. X-rays Sound wavesLight wavesripplesEarthquake or seismic wavesMicrowavesRadio wavesSurfing waveStadium waveUltrasound wavesWhat type of wave??? ME or EM EMMEMEMEMEMEMEEMEMEM
23. Transverse WavesWave that vibrates perpendicular to the direction of the wave’s motion. Crest – highest point on the waveWavelength – shortest distance between two identical points on a waveAmplitude – maximum distance from equilibrium (related to energy of the waveTrough – lowest point on the wave
24. Wave that vibrates parallel to the direction of the wave’s motion. Example: Vibrate a slinky back and forth Sound travels as longitudinal wavesLongitudinal Waves
25. Longitudinal Waves Transverse Waves Direction of travelDisturbanceDirection of travelDisturbance
26. Measurements of a WaveAmplitude – depends on source, not on speed or mediumPeriod/Frequency - depend on source, not on speed or mediumSpeed – depends only on medium (not on amp or frequency)Wavelength – depends only on medium Phasehttp://tdflashzone.net23.net/web_flash/wavemotion_v3.swf
27. Measuring a wave –
28. Measuring a wave – AMPLITUDE 2xs amp4xs energy
29. Period & Frequency Frequency – number of waves per secondMeasured in Hertz (Hz)Period – time it takes to complete one cycleMeasured in seconds (s)http://tdflashzone.net23.net/web_flash/wavemotion_v3.swf
30. Period & FrequencyThe frequency of a wave is equal to the reciprocal of the period.Both the period and the frequency of a wave depend only on its source. They do not depend on the wave’s speed or the medium.
31. Measuring a wave – Wavelength, llargeWavelengthmediumWavelengthsmallWavelengthll
32. Measuring a wave -speedSpeed of wave depends on the properties of the medium it travels ineg. Wave speed in a string depends on tension and strings mass/lengtheg. Wave speed in waterdepends on depth and g
33. Transverse WaveLongitudinal WaveA transverse wave is one that vibrates perpendicular to the direction of the wave’s motion.2) A quick shake of a rope sends transverse waves in both directions. 3) Waves obtained in threads and ropes are transverse waves. A longitudinal wave is one in which the particle displacement is in the same direction as, or parallel to, the direction of the wave’s motion.2) The squeeze and release of a coiled-spring toy sends out longitudinal wave pulses in both directions.3) Waves obtained in springs and sounds are longitudinal waves.
34. DO NOW a. What is the speed of the wave?b. What is the wavelength of the wave?c. What is the period of the wave?d. If the frequency was changed to 442 Hz, what would be the new wavelength and period? A sound wave has a frequency of 192 Hz and travels the length of a football field, 91.4 m, in 0.271 s. 337 m/s1.76 m0.0052 sSame medium so same v (337m/s)New T=0.0023s, new l=0.76m
35. The time required for the sound waves (v = 340 m/s) to travel from the tuning fork to point A is ____ .The wavelength of the sound is ______0.059 s0.664 m
36. a. one-ninthb. one-thirdc. the same asd. three times larger thanTwo waves are traveling through the same container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The speed of wave B must be ________ the speed of wave A.Same medium so same v
37. The water waves below are traveling along the surface of the ocean at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching? Answer and explain using complete sentences.
38. Suppose I wiggle a slinky back and forth, and count that 6 waves pass a point in seconds. What would the frequency be?f = 6 waves/2 sec = 3 waves/sec = 3 Hz
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40. Sound WavesSound is a type of wave.Longitudinal As the bell shown in the figure moves back and forth, the edge of the bell strikes particles in the air.
41. When the edge moves forward, air particles are driven forwardAir particles bounce with greater velocityGreater pressureWhen the edge moves backward, air particles are no longer driven forwardAir particles bounce with lower velocityLower pressure
42. This results in alternating regions of slightly high and slightly low pressure. The collisions among air particles cause the pressure variations to move away in all directions. These pressure variations are transmitted through matter as sound waves.
43. All Sound is Caused By Vibration of Something- Example - Sound Field radiated by a Tuning Forkhttp://www.betavakken.nl/natuurkunde/Applets/Golven%20en%20straling/Geluid/activity.swf
44. Properties of Sound Speed Pitch – frequency of sound Loudness – amplitude of sound Quality or timbre
45. PitchA measure of how high or low a sound isPitch depends on the frequency of a sound wave Low pitch Low frequency Longer wavelength High pitch High frequency Shorter wavelengthLouder(larger Amp)Softer(Smaller Amp)Phet sound and speaker sim
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47. Measurements of a WaveAmplitude – depends on source, not on speed or mediumPeriod/Frequency - depend on source, not on speed or mediumSpeed – depends only on medium (not on amp or frequency)Wavelength – depends only on medium Phasehttp://tdflashzone.net23.net/web_flash/wavemotion_v3.swf
48. Wave Behavior (all waves)When the wave encounters the boundary of the medium in which it is traveling, it often reflects back into the medium.In other instances, some or all of the wave passes through the boundary into another medium often changing direction - refraction.Many properties of wave behavior result from the fact that two or more waves can exist at the same time in the same medium (unlike particles).
49. Waves at Boundaries – wave speed depends on the mediumIncident Wave - wave that strikes the boundary Transmitted or Refracted Wave – wave that transmits to the new medium Reflected Wave – returning wave on the original medium
50. Reflection of WavesOccurs when a wave strikes a medium boundary and “bounces back” into original medium.Completely reflected waves have the same energy and speed as original wave.
51. Reflection from fixed boundaryReflects back - same speedInverted same amp
52. Reflection from free boundaryReflects back - same speed- upright
53. Refraction of WavesTransmission of wave from one medium to another.Refracted waves may change speed and wavelength.Refraction is almost always accompanied by some reflection.Refracted waves do not change frequency.
54. No boundaryRigid boundaryFree BoundaryLow to high density boundaryHigh to Low density boundaryWhen a wave encounters a boundary which is neither rigid (hard) nor free (soft) but instead somewhere in between, part of the wave is reflected from the boundary and part of the wave is transmitted across the boundary.
55. Reflection and Transmission of WavesslowerslowerSame speedsame
56. Reflection and Transmission of WavesSame speedfasterHigh to Low density boundary
57. Reflection and Transmission of WavesReflected waveSame speedRefracted wave slowerHigh to Low density boundaryMORE denseLESS dense
58. Reflection and Transmission of WavesRefracted wave fasterHigh to Low density boundaryMORE denseLESS denseReflected waveSame speed
59. Reflection and Transmission of WavesReflectedTransmittedSpeed (l)*samefasterwaveformuprightuprightamplitudesmallerlargerMORE denseMORE denseLESS denseLESS denseReflectedTransmittedSpeed (l)*sameslowerwaveforminverteduprightamplitudelargersmaller*Transmitted waves DO NOT change frequency
60. DO NOWThe speed of sound in water is 1498 m/s. A sonar signal is sent straight down from a ship at a point just below the water’s surface, and 1.80 s later, the reflected signal is detected. How deep is the water? 1348.2m = 0.84 mile
61. DO NOW 0.1m1m/s0.1mvreflectedvtransmitted2cmTOP: An incident pulse is traveling at a speed of 1 m/s in a string (blue) to which a 2nd string of a different density (red) is attached. BOTTOM: Part of the wave is reflected at the boundary and part is transmitted. What is the amplitude of the incident pulse?What are the wavelengths of the incident, reflected and transmitted pulses?What are the frequencies of the incident, reflected and transmitted pulses?What are the speeds of the reflected and transmitted pulses?Which string is denser, the blue or the red one?4 cmli=0.8m, lr=0.8m, lt=0.4m1.25hzvr=1m/s, vt=0.5m/sRed
62. Superposition of Waves When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the sum of the displacements due to each individual wave.The waves interfere with each other. http://www.cabrillo.edu/~jmccullough/Applets/Flash/Fluids,%20Oscillations%20and%20Waves/StandingWaveExplanation.swf
63. Wave InterferenceDestructive Interference – wave displacements in opposite directionConstructive Interference – wave displacements in same directionAntinodeNodehttp://zonalandeducation.com/mstm/physics/waves/interference/waveInterference1/WaveInterference1.html
64. Principle of SuperpositionThe displacement of a medium caused by two or more waves is the algebraic sum of the displacements caused by the individual waves. In other words, two or more waves can combine to form a new wave - interference. Constructive interference – result in a new wave with greater amplitude.Destructive interference – result in a new wave with lesser amplitude.
65. Wave Interferencehttp://zonalandeducation.com/mstm/physics/waves/interference/waveInterference2/WaveInterference2.html http://earthguide.ucsd.edu/earthguide/diagrams/wave_interference/wave_interference.html
66.
67. Standing WavesA standing wave is a wave which is reflected back and forth between fixed ends (off a string or pipe, for example).Reflection may be fixed or open-ended.Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave.https://www.youtube.com/watch?v=-n1d1rycvj4 https://www.youtube.com/watch?v=-gr7KmTOrx0
68. Standing WavesWave that appears to be standing still.Standing wave is the interference of two traveling waves (with equal f and l), moving in opposite directions. Nodes are at the ends of the rope.Antinodes are in the middle.
69. Standing WavesIf you double the frequency of the vibration, you can produce one more node and one more antinode in the rope. Further increases in frequency produce even more nodes and antinodes.http://www.walter-fendt.de/ph14e/stwaverefl.htm
70. ResonanceResonance is a special form of simple harmonic motion in which the additions of small amounts of force at specific times in the motion of an object cause a larger and larger displacement.Resonance from wind, combined with the design of the bridge supports, may have caused the original Tacoma Narrows Bridge to collapse.London Millenium bridge Tacoma Narrows Bridge Tacoma Narrows Bridge2 https://www.youtube.com/watch?v=JiM6AtNLXX4 glass shattering montage
71.
72. Standing WavesNodes Poinst of complete destructive interference Do not moveAntinodes Poinst of complete constructive interference Largest amplitude points of the standing waveIncident waveReflected wave
73. Fixed end Standing Waves (violin string)First Harmonic Standing Wave Pattern Third Harmonic Standing Wave Pattern 1st harmonic L= ½l= ½ v/f12nd harmonic (one octave higher) L= l= v/f23rd harmonic L= 3/2 l = 3/2 v/f3 http://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves1/StandingWaves1.html If a guitar string is simply plucked, the fundamental frequency dominates. The first harmonic can be produced by touching the string lightly in the middle when plucking it. Touching the string lightly one-third the length of the string from one end will produce the second harmonic
74. Harmonic# of Nodes# of AntinodesPatternResonant Frequency1st21L = l1/2 = v/2f12nd32L = l2= v/f2 f2 =2f13rd43L = 3l3/2 = 3v/2f3 f3 = 3f14th54L = 2l4= 2v/f4 f4 = 4f15th65L = 5l5/2 = 5v/2f5 f5 = 5f16th76L = 6l6 /2= 3v/f6 f6 = 6f1nthn + 1n--L = nln/2= nv/2fn fn = nf1Standing WavesFirst Harmonic Standing Wave Pattern Second Harmonic Standing Wave Pattern Third Harmonic Standing Wave Pattern http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html guitar strings
75. Example: If a violin string vibrates at 440 Hz as its fundamental frequency, what are the frequencies of the first four harmonics
76. Example: ViolinA 0.32 m long violin string is tuned to play A above middle C at 440 HzWhat is the wavelength of the fundamental string vibration?1st harmonic L= ½l1
77. Wind Instruments Sound is generated by vibrations, so when air is blown into one end of a pipe or tube and then bounces off of the sides, the air vibrates. When the air inside the tube vibrates at the same frequency, or in resonance, with the vibration of your lips, a sound is produced.
78. Wind Instruments The vibrating reed or lip produces sound waves with many frequencies. This sound wave of alternate high- and low-pressure variations moves down the air column. When the wave reaches the end of the column, it is reflected back up the column and can set up standing waves.
79. Resonance in an Open PipeEnds must be same - both ends are pressure nodes (displacement antinodes) Harmonics increase by 1: 1st, 2nd, 3rd, 4th, 5th, etc.1st HarmonicL = l1/22nd HarmonicL = l23rd HarmonicL = 3l3/2nth HarmonicL = nln/2…Pressurenodessound wave in pipes Pressurenodes
80. Resonance in a Closed PipeEnds must be opposite: open–nodes, closed-antinodes Harmonics increase by 2 (only odd harmonics).1st HarmonicL = l1/4 = v/4f13nd HarmonicL = 3l3/4 = 3v/4f3 f3 = 3f15th HarmonicL = 5l5/4 = 5v/4f5 f5 =5f1nth Harmonic (odd only)L = nln/4 = nv/4fn fn = nf1…PressurenodePressureantinodehttp://zonalandeducation.com/mstm/physics/waves/standingWaves/standingWaves3/StandingWaves3.html
81. Closed PipesEnds are oppositeOdd HarmonicsOpen Pipeshttp://www.phys.unsw.edu.au/jw/flutes.v.clarinets.html ShakuhachiEnds sameEvery HarmonicPan PipesClarinetTrumpetFluteSax
82. Do NowFor an open tube with a length of 0.3 m,a) What is the fundamental resonant frequency?b) What is the frequency of the 2nd harmonic? The speed of sound waves in the tube is 343 m/sOPEN PIPE1st Harmonicf1 = 572 Hz2nd Harmonicf2 = 1143 Hz (= 2f1)1st2nd3rd
83. Do NowClosed PIPEFor closed tube with a length of 2 m,a) What is the fundamental resonant frequency?b) What is the frequency of the 3rd harmonic? The speed of sound waves in the tube is 343 m/s1st Harmonicf1 = 42.88 Hz2nd Harmonicf3 = 128.6 Hz (= 3f1)1st3rd
84. Determine the length of a closed-end air column that produces a fundamental frequency (1st harmonic) of 480 Hz. The speed of waves in air is known to be 340 m/s. Draw a diagram to help you solve.1st Harmonicv = 340 m/sf = 480 HzL
85. The lead instrumentalist of a band uses a test tube (closed-end air column) with a 17.2 cm air column. The speed of sound in the test tube is 340 m/sec. Find the frequency of the first harmonic played by the instrument.1st HarmonicL=0.172mf1=494 Hz
86. Doppler Effect
87. Stationary Sound source emitting sound with frequency fsI hear fsI hear fs
88. Doppler EffectSound source moving with vs emitting sound with frequency fsI detect lower pitch fO< fsI detect higher pitch fO>fs
89. Breaking the Sound BarrierSound source moving at the speed of sound (Mach 1) emitting sound with frequency fsI detect lower pitch fo< fsOW, I hear sonic BOOM
90. SupersonicSound source moving faster than the speed of sound (Mach 1.4) emitting sound with frequency fsI detect lower pitch fo< fsOW, I hear sonic BOOMhttp://www.youtube.com/watch?feature=player_detailpage&v=-d9A2oq1N38
91. + Observer moving towards- Observer moving away+ Source receding- Source approachingDoppler Effect
92. Doppler EffectThe Doppler effect occurs in all wave motion, both mechanical and electromagnetic.Astronomers observe light from distant galaxies and use the Doppler effect to measure their speeds and infer their distances.Radar detectors use the Doppler effect to measure the speed of baseballs and automobiles. Physicians can detect the speed of a moving heart wall in a fetus by means of Doppler effect in an ultrasound.
93. Doppler EffectA trumpet player sounds C above middle C (524 Hz) while traveling in a convertible at 24.6 m/s. If the car is coming toward you, what frequency would you hear? Assume that the temperature is 20°C.Fs = 524 Hzvs = 24.6 m/s
94. Doppler EffectA trumpet player sounds C above middle C (524 Hz) while traveling in a convertible at 24.6 m/s. Once the car passes and is going away from you, what frequency would you hear? The speed of sound is 343 m/s.Fs = 524 Hzvs = 24.6 m/s
95. One foggy morning, Benny is driving his speed boat toward a lighthouse as the fog horn blows with a frequency of 180.0 Hz. As he approaches, he hears a frequency of 188 Hz. What speed is Kenny traveling to hear this change in frequency? The speed of sound in air is 343 m/s.Givens: fs = 180HzfO = 188 Hzv = 343 m/svs = 0
96. http://www.tutorvista.com/content/physics/physics-i/wave-motion-sound/echo-location.php Echolocation tutorial