Essential Knowledge 3B3 Restoring forces can result in oscillatory motion When linear restoring force is entered on an object displacement from an equilibrium position the object will undergo a special type of motion called simple harmonic motion SMH ID: 1015949
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1. Waves AP Physics 1
2. StandardsEssential Knowledge 3.B.3: Restoring forces can result in oscillatory motion. When linear restoring force is entered on an object displacement from an equilibrium position, the object will undergo a special type of motion called simple harmonic motion (SMH). -Examples should include gravitational force exerted by earth on a simple pendulum and mass- spring oscillator. a. For a spring that exerts a linear restoring force, the period of a mass-spring oscillator increases with mass and decreases with spring stiffness. b. For a simple pendulum, the period increases with the length of the pendulum and decreases with the magnitude of the gravitational field. c. Minima, maxima, and zeros of position, velocity, and acceleration are features of harmonic motion. Students should be able to calculate force and acceleration for any given displacement for an object oscillating on a spring.
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4. What is a wave? -A disturbance that propagates through space or a medium, and transports energy without transporting mass.
5. What is a Pulse? -A single vibratory disturbance that propagates through space or a medium, and transports energy and information but no mass.
6. Types of waves:Waves are classified into different types accordingly :
7. Mechanical Waves -A material is needed for the transmission. -Cannot travel through vacuum.Ex: Water waves, sound, vibration of spring
8. Electromagnetic Waves No medium is needed for propagation. They can travel through a vacuum. All electromagnetic waves are transverse.Ex: X-rays, radio waves, micro-waves,etc
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10. Transverse WavesAppears as a sine curve.The motions of the particles is Perpendicular to the direction of energy propagation – the direction the wave is movingEx: Pulse in a stretched string, light.
11. Longitudinal Waves 1. The motions of the particles is parallel to the direction that the energy propagates – the direction the wave travels.Ex: Sound, or a spring oscillating back and forth.
12. Longitudinal waves In sound the particles of the medium move back and fort creating regions of high and low density ,or high or low pressure,Condensations ( High Pressure) and Rarefactions (Low Pressure).
13. Types of waves:MechanicalElectromagneticMechanical Wavesocean wavesseismic wavessound wavesElectromagnetic Wavesradio wavesx-rayslight
14. Wave Speed - The speed depends on the “medium” it’straveling in and the temperature. Type (temp) SpeedSound in air at 20°C 343 m/s = 767 miles/hourSound in air at 0°C 331 m/sSound in water at 25°C 1493 m/sSound in aluminum 5100 m/sLight in vacuum 3 x 108 m/s = 186,000 miles/secLight in diamond 1.2 x 108 m/s
15. Wave Properties - A wave is described in terms of thefollowing characteristics:AmplitudeWavelength ( )Frequency (f )Period (T)Wave velocity (v)CrestTroughCompressionRarefactionNodes
16. Period and Frequency Period ( T ) - Is the time it takes to complete one oscillation or vibration (measured in seconds) (sec/cycle)Frequency - ( f ) the number of vibrations, oscillations or waves per unit time. (measured in 1/s or hertz) (cycles/sec)
17. Period and Frequency are inverse of one another.
18. Amplitude - Maximum displacement from its equilibrium position.Wavelength ()- The minimum distance between two points which are in phase.
19. AmplitudeFrequencySound WavesLoudnessPitchLightWavesBrightness ROYGBIVCOLORRed - Lowest frequency - Longest wavelengthViolet -Highst frequency - Shortest wavelength
20. Wave EquationThe wave velocity is the displacement traveled by the wave in one second …….... The velocity of the wave (v) is related to frequency (f) and wavelength () by -
21. A wave travels one wavelength in one period. Thus, the speed (v):Wave Equation DerivationSince
22. A traveling wave of wavelength 1.0 m moves at a speed of 3.0 m/s.What is the period of this wave?What is the frequency of this wave?By using the wave equation, v = ƒ 3.0 m/s = ƒ(1.0 s) ƒ = 3.0 HzPeriod T = 1/ƒ T = 1/3 Hz T= .333 sec
23. The diagram shows a piston being moved back and forth to generate a wave.The piston produces a compression, C , every 0.50 second. The frequency of this wave is1.0 Hz2.0 Hz5.0 x 10-1 Hz3.3 x 102 HzWhat is the angle between the direction of propagation of a transverse wave and the direction in which the amplitude of the wave is measured?0 degrees45 degrees90 degrees180 degrees
24. What is the period of a periodic wave that has the frequency of 60 hertz?1.7 x 10-2 s2.0 x 104 s3.0 x 10-3 s3.3 x 102sA periodic wave with a frequency of 10 hertz would have a period of:1s0.1s10s100s
25. The echo is heard 2 seconds after a sonar wave reflects off the ocean floor which is 1170 meters awayWhat is the waves speed ? If the frequency of the wave is 60Hz, what is it’s wavelength? What is the period of the wave?
26. A skipper on a boat notices wave crests passing his anchor chain every 5 seconds. If the wave crests are 15 m apart, what is the speed of the water waves in m/s? 51575103
27. An elephant produces a 10 Hz sound wave. Assuming the speed of sound in air is 345 m/s, determine the wavelength of this infrasonic sound wave.
28. Miles Tugo is camping in Glacier National Park. In the midst of a glacier canyon, he makes a loud holler. He hears an echo 2.0 s later. The air temperature is 200 C. How far away are the canyon walls. Two sound waves are traveling through a container of nitrogen gas. Wave A has a wavelength of 1.5 m. Wave B has a wavelength of 4.5 m. The velocity of wave B must be _______ the velocity of wave A.one-ninthone-third the same asthree times larger than
29. Speed of a Wave on a StringThe speed on a wave stretched under some tension, Fm is called the linear densityThe speed depends only upon the properties of the medium through which the disturbance travelsSection 13.9
30. Constructive InterferenceTwo waves, a and b, have the same frequency and amplitudeAre in phaseThe combined wave, c, has the same frequency and a greater amplitudeSection 13.10
31. Constructive Interference in a StringTwo pulses are traveling in opposite directionsThe net displacement when they overlap is the sum of the displacements of the pulses*Note that the pulses are unchanged after the interference
32. Destructive InterferenceTwo waves, a and b, have the same amplitude and frequencyOne wave is inverted relative to the otherThey are 180° out of phaseWhen they combine, the waveforms cancel
33. Two pulses are traveling in opposite directionsThe net displacement when they overlap is decreased since the displacements of the pulses subtract*Note that the pulses are unchanged after the interferenceDestructive Interference in a String
34. Reflection of Waves – Fixed EndWhenever a traveling wave reaches a boundary, some or all of the wave is reflectedWhen it is reflected from a fixed end, the wave is invertedThe shape remains the same
35. Reflected Wave – Free EndWhen a traveling wave reaches a boundary, all or part of it is reflectedWhen reflected from a free end, the pulse is not inverted
36. Polarization: the limiting of a vibrations of a wave to a single plane. Only transverse wave may be polarized. Waves may be polarized by Generation Filtering Reflection
37. Polarization of LightElectromagnetic waves are transverse wavesTransverse waves are polarizableLongitudinal waves, like sound waves, cannot be polarized
38. Polarizing filters:Enhance blue skies and increase color saturation by reducing reflections Reduce glare on streams and wet leaves. Non PolarizedThe unpolarized image looks flat, without saturated colors. PolarizedNotice the more saturated colors, the blue in the sky and the colors in the trees. There is also a greater sense of depth and perspective.
39. The Doppler effect is the way a wave seems to increase or decrease in frequency when there is relative motion between the observer and the source of the wave.Have you ever stopped at a railroad crossing to let a train pass by? Did you notice that the sound of the train's whistle is higher pitched when the train was approaching and lower when it was receeding? Then you have witnessed the Doppler effect.Doppler Acapella (Link)
40. When a source of waves and an observer are moving towards each other:A higher frequency is heardA shorter wavelength is observed.When a source of waves and an observer are moving apart:A lower frequency is heardA longer wavelength is observed.Roy G Biv
41. Weather radars send out radio waves. Objects in the air, such as rain drops, snow crystals, hail stones or even insects and dust, scatter or reflect some of the radio waves back to the antenna. Weather radars electronically convert the reflected radio waves into pictures showing the location and intensity of precipitation. Doppler radars also measure the frequency change in returning radio waves. Waves reflected by something moving away from the antenna change to a lower frequency. Waves from an object moving toward the antenna change to a higher frequency.
42. A particularly interesting example is used by astronomers to determine if Light emitting objects (such as stars) are getting closer to us or farther away. 1. If light (star) is moving away – lower frequency, long wavelength– red shifted 2. If light (star) is moving towards – higher frequency, short wavelength – blue shifted.LIGHT
43. Red Shift
44. Case I: Stationary wave source
45. Case II: Wave velocity greater than the source velocity.
46. Case III: Wave velocity the same as the source velocity
47. Case IV : Wave velovity less than the source velocity(sound-sonic boom!).
48. DOPPLER EFFECT AND SOUNDWhen you move away from a fixed source of sound the frequency of the sound you hear:is greater than what the source emitsis less than what the source emitsis the same as what the source emits
49. A train whistle at rest has a frequency of 3000 Hertz. You are standing still and observe the frequency to be 3010 Hz, you can conclude that...a. the train is moving away from youb. the train is moving toward youc. the sound from the whistle has echoedd. not enough information is given
50. Doppler Effect, General CaseBoth the source and the observer could be movingUse positive values of vo and vs if the motion is towardFrequency appears higherUse negative values of vo and vs if the motion is awayFrequency appears lowerSection 14.6
51. Doppler Effect, Source Moving – EquationUse the –vs when the source is moving toward the observer and +vs when the source is moving away from the observerSection 14.6
52. Doppler Effect, Source Moving – EquationUse the –vs when the source is moving toward the observer and +vs when the source is moving away from the observerSection 14.6
53. Occurs when energy is transferred to a system ... at its natural frequency. Resonance
54. Natural Frequency...Object composed of elastic material will vibrate at a natural frequency when disturbedThe natural frequency of a body depends on its ...ElasticitySizeshapeResonance
55. Resonance occurs in all types of objectsWhen the applied frequency…..matches the natural frequency of the body.The resulting vibration has a high amplitude possibly destroying the body.
56. mass on a spring at resonanceswinging your legs in a swingbreaking a wine glass using sounda tuning fork exciting a guitar stringa truck driving on a rough roadIn 1940, the Tacoma Narrows Bridge was destroyed by wind-generated resonance.
57. Resonance in a rulerHold a 30 cm rule loosely at one end between your thumb and first finger. Tap it and let it swing from side to side, so the frequency is about 1 Hz. Now try to keep the ruler swinging at the frequency. You should be able to do this with very slight hand movements.Notice how easy it is to get the ruler to make swings with a large amplitude.Without putting more effort into it, try to doubled the frequency of your hand movement. What has happened to the amplitude of the ruler's swing? Probably much smaller.If you’ve still got the same amplitude you may be putting in more effort than before. You will also get a smaller amplitude from the ruler if you decrease the frequency of your hand movement to well below 1 Hz.
58. Resonance in your bathroom. The air in your bathroom will have a resonant frequency. This means that if you hum notes of different pitches, one of them will sound louder than all the others. At this frequency the air is resonating, it’s oscillating with a bigger amplitude. So when you talk in there, your voice may sound a bit different - usually a bit boomy. Whilst this is fine in a bathroom, we don't want this effect in a loudspeaker.
59. If you push a person on a swing, you must put the energy in at just the natural frequency of the swing. In this animation, the energy is put in at the natural frequency of the pendulum. Notice how the energy builds constructively until it does work on the monkey's face.If you put the energy in too slow, you miss the swing being there to accept the energy. If you put it in too fast, you miss the swing more often. In this case the energy is put in at higher than the natural frequency of the pendulum. As a result of the destructive energy, the energy level does not build up.
60. If there is a second tuning fork nearby with the same Natural Frequency it will begin to vibrate also even though it hasn’t been struck."SYMPATHETIC VIBRATIONS"
61. Tacoma Narrows Bridgelink
62. Resonance allows energy to be transferred to a vibrating object efficiently if the energy is delivered at the natural frequency of vibration.Tacoma Narrows Bridge
63. How Earthquakes Make Buildings VibrateResonance in Buildings If the ground moved to and fro with a frequency of 5.5 Hz Tall building would vibrate strongly, or resonateShort building hardly moved.If the ground shook with a frequency of 7.5 Hertz, the small building would resonate while the tall building hardly moved at all.
64. Taller buildings tend to have a lower natural frequency than shorter buildings because they are more flexible. Buildings tend to have lower natural frequencies when they are heavier or more flexible.
65. Beat FrequencyBeats are used to tune up musical instruments!BEATS: When two waves of slightly different frequencies interfere with each other.
66. The beat frequency is equal to the difference in the frequency of the two sounds.What is the beat frequency when a 262 Hz and a 266 Hz tuning fork are sounded together?What is the period of the beat in the previous problem?
67. One speaker is transmitting a 10 Hz signal and a second istransmitting a 11 Hz signal. What beat frequency is experienced?
68. The waves interfere with each other alternatively constructive and destructive.