1. Physics is Life1 Chapter 15 Energy Transfer by Wave 1Physics is Life

2. 2 Sound of Waves 2Physics is Life

3. 3 Wave Motion What is a Wave? A wave can be described as a disturbance that travels through a medium from one location to another location. Examples: Sound, water, light, microwaves, and heat waves 3Physics is Life

4. 4 Wave Motion Waves transfer energy from one place to another with no transfer of mass. Waves can be produced in two ways: (a) Vibration of particles (requires a medium) Ex. Sound, water, spring (b) Small changes in the electromagnetic Field. (requires no medium for transfer) Ex. Light, microwaves, x rays. Animation: http://www.cs.sbcc.cc.ca.us/~physics/flash/electricfieldwaves2.html 4Physics is Life

5. 5 Wave Motion What is a medium? A medium is a substance or material which carries the wave. You have perhaps heard of the phrase news media. The news media refers to the various institutions (newspaper offices, television stations, radio stations, etc.) within our society which carry the news from one location to another. The news moves through the media. The media doesn't make the news and the media isn't the same as the news. The news media is merely the thing that carries the news from its source to various locations. In a similar manner, a wave medium is the substance which carries a wave (or disturbance) from one location to another. 5Physics is Life

6. 6 The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations. In the case of a slinky wave, the medium through which the wave travels is the slinky coils. In the case of a water wave in the ocean, the medium through which the wave travels is the ocean water. In the case of a sound wave, the medium through which the sound wave travels is the air in the room. Wave Motion 6Physics is Life

7. 7 Parts of Wave Motion Amplitude, A : The maximum displacement of a vibrating wave Wavelength, λ : The distance from a point of a wave to the corresponding point of the succeeding wave Frequency f : Number of cycles per second (units are Hertz) Period T : The time required for one vibration, cycle, or one oscillation (Note that T = 1/f). Wave velocity, v, where v = fλ and f = 1/T How changing the amplitude and frequency affect wave motion 7Physics is Life

8. 8 Standing Waves A standing wave is a wave that appears standing still. Standing waves are produced by the interference of two traveling waves moving in opposite directions. There are nodes, where the amplitude is always zero, and antinodes, where the amplitude varies from zero to the maximum value. Standing Waves Animation Standing waves tutorial 8Physics is Life

9. 9 Wave Motion Sample Problem Water waves in a shallow dish are 6.0cm long. At one point the water oscillates up and down at a rate of 4.8 oscillations per second. (a) What is the speed of the wave? (b) What is the period of the water waves? Solution (a) v = f = (0.060m)(4.8 Hz) = 0.29 m/s (b) T= 1/f = 1/4.8Hz = 0.21s 9Physics is Life

10. 10 Wave Motion Sample Problem A sound wave has a frequency of 262 Hertz and wavelength ( ) measured at 1.29m. (a) What is the speed (v) of the wave? (b) How long will it take the wave to travel the length of a football field, 91.4m? © What is the period of the wave? Solution (a) Find the speed of sound from the frequency and wavelength. v= f= (1.29m)(262Hz) = 338m/s (b) Find the time required from speed and distance. V=d/t, so t=d/v thus, t = 91.4m/338 m/s = 0.270 s © Find the period from the frequency. T = 1/f = 1/262z = 0.00382s 10Physics is Life

11. 11 Waves are everywhere in nature –Sound waves, –visible light waves, –radio waves, –microwaves, –water waves, –sine waves, –telephone chord waves, –stadium waves, –earthquake waves, –waves on a string, –slinky waves 11Physics is Life

12. 12 Slinky Wave Let’s use a slinky wave as an example. When the slinky is stretched from end to end and is held at rest, it assumes a natural position known as the equilibrium or rest position. To introduce a wave here we must first create a disturbance. We must move a particle away from its rest position. 12Physics is Life

13. 13 Slinky Wave One way to do this is to jerk the slinky forward the beginning of the slinky moves away from its equilibrium position and then back. the disturbance continues down the slinky. this disturbance that moves down the slinky is called a pulse. if we keep “pulsing” the slinky back and forth, we could get a repeating disturbance. 13Physics is Life

14. 14 Two Types of Wave Motion: Transverse and Longitudinal A transverse wave is sometimes called a shear wave, because the disturbance supplies a force that tends to shear the medium-to separate layers of that medium at a right angle to the direction of the wave velocity. Shear waves can propagate only in solids, since a liquid or a gas does not have sufficient restoring forces between its particles as to propagate a transverse wave. A longitudinal wave can propagate in solids liquids and gases, since all phases of matter can be compressed to some extent. http://Transverse vs. Longitudinal WavesTransverse vs. Longitudinal Waves Animation of Transverse, Longitudinal and other waves 14Physics is Life

15. 15 Transverse vs Longitudinal Waves The differences between the two can be seen: 15Physics is Life

16. 16 Longitudinal Wave The wave we see here is a longitudinal wave. The medium particles vibrate parallel to the motion of the pulse. This is the same type of wave that we use to transfer sound. Can you figure out how?? 16Physics is Life

17. 17 Transverse waves A second type of wave is a transverse wave. We said in a longitudinal wave the pulse travels in a direction parallel to the disturbance. In a transverse wave the pulse travels perpendicular to the disturbance. 17Physics is Life

18. 18 Types of Wave Motion : Transverse and Longitudinal In summary, the motion of particles in a wave can either be perpendicular to the wave direction (transverse) or parallel to it (longitudinal). 18Physics is Life

19. 19 Check your Understanding What is a wave? What is a pulse? Name some of the important parts of a wave. Define a standing wave? Describe the difference between the nodes and the antinodes of a standing wave Elucidate the difference between longitudinal and transverse waves. Write an equation that describes how the velocity, frequency and wavelength of a wave are related. 19Physics is Life

20. 20 Wave Behavior We know that waves travel through mediums. But what happens when that medium runs out? 20Physics is Life

21. 21 Boundary Behavior The behavior of a wave when it reaches the end of its medium is called the wave’s BOUNDARY BEHAVIOR. When one medium ends and another begins, that is called a boundary. 21Physics is Life

22. 22 Fixed End One type of boundary that a wave may encounter is that it may be attached to a fixed end. In this case, the end of the medium will not be able to move. What is going to happen if a wave pulse goes down this string and encounters the fixed end? 22Physics is Life

23. 23 Fixed End Animation 23Physics is Life

24. 24 Fixed End Here the incident pulse is an upward pulse. The reflected pulse is upside-down. It is inverted. The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse. 24Physics is Life

25. 25 Free End Another boundary type is when a wave’s medium is attached to a stationary object as a free end. In this situation, the end of the medium is allowed to slide up and down. What would happen in this case? 25Physics is Life

26. 26 Free End Animation 26Physics is Life

27. 27 Free End Here the reflected pulse is not inverted. It is identical to the incident pulse, except it is moving in the opposite direction. The speed, wavelength, and amplitude are the same as the incident pulse. 27Physics is Life

28. 28 Change in Medium Our third boundary condition is when the medium of a wave changes. Think of a thin rope attached to a thin rope. The point where the two ropes are attached is the boundary. At this point, a wave pulse will transfer from one medium to another. What will happen here? 28Physics is Life

29. Change in Medium Animation http://www.stmary.ws/highschool/physics/home/notes /waves/intro/video/slinkyreflections2.mov 29Physics is Life

30. 30 Change in Medium In this situation part of the wave is reflected, and part of the wave is transmitted. Part of the wave energy is transferred to the more dense medium, and part is reflected. The transmitted pulse is upright, while the reflected pulse is inverted. 30Physics is Life

31. 31 Change in Medium The speed and wavelength of the reflected wave remain the same, but the amplitude decreases. The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse. 31Physics is Life

32. 32 Wave Interaction All we have left to discover is how waves interact with each other. When two waves meet while traveling along the same medium it is called INTERFERENCE. 32Physics is Life

33. 33 Constructive Interference Let’s consider two waves moving towards each other, both having a positive upward amplitude. What will happen when they meet? 33Physics is Life

34. 34 Constructive Interference They will ADD together to produce a greater amplitude. This is known as CONSTRUCTIVE INTERFERENCE. 34Physics is Life

35. 35 Destructive Interference Now let’s consider the opposite, two waves moving towards each other, one having a positive (upward) and one a negative (downward) amplitude. What will happen when they meet? 35Physics is Life

36. 36 Destructive Interference This time when they add together they will produce a smaller amplitude. This is know as DESTRUCTIVE INTERFERENCE. 36Physics is Life

37. 37 Interference; Principle of Superposition The superposition principle says that when two waves pass through the same point, the displacement is the arithmetic sum of the individual displacements. In the figure below, (a) exhibits destructive interference and (b) exhibits constructive interference. 37Physics is Life

38. 38 Interference; Principle of Superposition These figures show the sum of two waves. In (a) they add constructively; in (b) they add destructively; and in (c) they add partially destructively. http://www.stmary.ws/highschool/physics/home/notes/waves/WaveBehavior/InterferenceIntro.htm http://www.stmary.ws/highschool/physics/home/review/outsid eContent/waves/InterferenceropeMontereyInstitute.htm 38Physics is Life

39. 39 Waves that are in and out of Phase "In Phase" (0°) – points on a single periodic wave that have the same displacement (from equilibrium position) and moving in the same direction. It must be a Whole number of wavelengths apart. For example A & E, A & I, B &F and B &N are in phase "Out of Phase"– (180º) - same displacement from equilibrium position but going in a different direction It must be ½, 1½, 2½ etc wavelengths apart. For example A &C, B & D, F &H are out of phase. 39Physics is Life

40. 40 Standing Waves: Revisited If you shake one end of a cord and the other end is kept fixed, a continuous wave will travel to the fixed end and be reflected back, inverted. As you continue to vibrate the cord, there will be waves traveling in both directions, and the wave traveling down the cord with interfere with the reflected wave coming back. Usually there will be quite a jumble. But if you vibrate the cord at just the right frequency, the two traveling waves will interfere in such a way that a large amplified standing wave will be produced. The frequencies at which standing waves are produced are the natural frequencies or resonate frequencies of the cord. A standing wave produced on a cord is an example of a vibrating object at resonance.resonance In resonance the oscillation occurs at a specific frequency. These oscillations build up rapidly to very high levels. Ultimately some of the energy in the oscillations has to be removed from the object or the size of the oscillations get so large that the object breaks The Physics of Resonance 40Physics is Life

41. 41 Forced Vibrations; Resonance Forced vibrations occur when there is a periodic driving force. This force may or may not have the same period as the natural frequency of the system. When the forcing function's frequency matches the natural frequency of an object it will begin to resonate. The forcing function adds energy at just the right moment during the oscillation cycle so that the oscillation is reinforced. This makes the oscillation's amplitude grow larger and larger. These oscillations would eventually become infinitely large. An example of this is pushing a child on a swing. MIT LECTURE ON FORCED VIBRATIONS 41Physics is Life

42. 42 Forced Vibrations; Resonance Resonance can be wanted or unwanted. The collapse of the Tacoma Narrows Bridge in 1940 was due in part to resonance of the bridge (in tune with wind gusts) Short Video of this disaster 42Physics is Life

43. Forced Vibrations; Resonance Breaking wine glass with sound#1 Wine glass music MIT LECTURE ON WAVES AND RESONANCE The Mechanical Universe Video: Resonance 43Physics is Life Breaking wine glass with sound#2

44. Physics is Life44 What Is Sound? "If a tree falls were to fall in a forest and no living thing is around to hear it, does it make a sound?"

45. Physics is Life45 "Sound is vibration, transmitted to our senses through the mechanism of the ear, and recognized as sound only at our nerve centers. The falling of the tree or any other disturbance will produce vibration of the air. If there be no ears to hear, there will be no sound." "Sound is an organized movement of molecules caused by a vibrating body in some medium - water, air, rock, etc.”Sound "Sound is the auditory sensation produced through the ear by the alteration... in pressure, particle displacement, or particle velocity which is propagated in an elastic medium." What Is Sound? Outer ear collects sound energy, bones in middle ear transmit vibrations to fluid in canals (the inner ear). Canals in cochlea separated by a flexible partition which flexs at different points depending on the frequency; nerve hairs in canals send information to the brain.

46. The Nature of a Sound Wave Sound originates when a body moves back and forth rapidly enough to send a coursing wave through the medium in which it is vibrating. If there is no medium, there is no sound. Therefore, sound cannot travel through a vacuum. *Electromagnetic waves, i.e. light can travel in a vacuum. 46Physics is Life The production of sound requires 3 things: A source, a medium, and a receiver. The source, through vibrations called "compression" and "rarefraction", creates a series of pressure waves that vary in frequency and amplitude. These pressure waves propagate through various mediums including water, air and solids. The receiver collects and converts these pressure waves into electrical impulses. If you remove any of the 3 requirements for sound, there is no sound. More on Sound 46Physics is Life

47. 47 Is there sound in outer space? NO. In the vacuum of space, however, there is no air or any other medium, and therefore sound cannot travel. Light can travel through space because light is a waveform that is part of the electromagnetic spectrum (which includes radio waves, microwaves and x rays) and electromagnetic waves do not need a medium in which to travel. The absence of sound in space is often forgotten in cheap science fiction movies where an alien spaceship is exploded and you hear the loud bang. In real life this would never happen. The best depiction of space and the absence of sound in it is in Arthur C Clarke's 2001: A Space Odyssey directed by Stanley Kubrick. Although it is one of the greatest science fiction movies of all time, it was criticized because of periods of silence during the 'space' scenes - but of course this was a factually accurate depiction as opposed to the cheap sci-fi 'B' movies where enemy ships explode in a flash of light and a huge bang.

48. PITCH Molecules in the air vibrate about some average position creating the compressions and rarefactions. The distance between any two “compressed” regions is the wavelength,. If you know the velocity of the wave as well as the wavelength, one can calculate the frequency ( f = v/ ). We call the frequency of sound the pitch. 48Physics is Life48Physics is Life

49. Speed of Sound Depends on the material of the vibrating medium Sound can vibrate water, wood (speaker enclosures, pianos), metal, plastic, etc. Sound speed in dry air is 330 meters/second at 0 o C Faster in warm air, slower in cold Water 4 times faster, steel 15 times faster 49Physics is Life49Physics is Life

50. 50 Velocity of Sound in air Varies with temperature Greater kinetic energy -> sound impulse transmitted faster Increase factor (units!): 0.6 m/s/°C; 2.0 ft/s/°C Physics is Life

51. Sound waves move faster through a denser medium because energy is more easily passed between tightly packed molecules. This helps explain why sound travels faster through water than through air, and faster still through steel than through water. But even more influential than a conducting medium's density is its elasticity. Elasticity refers to how well a medium can return to its initial form after being disturbed by a force. Steel has high elasticity. It bounces right back to its original shape after an applied force is removed. At the particle level, the molecules in elastic materials transfer energy more efficiently, so sound waves travel faster through steel than through water or air. But not all solids are good conductors of sound. Cork, for instance, has low elasticity. Its molecules tend to absorb energy rather than conduct it. Air, a mixture of gases, is less elastic than most solids and all liquids. Despite being the standard medium through which we hear sounds, it is actually a relatively poor conductor. Physics is Life51 Velocity of Sound in Solids vs. Air http://www.teachersdomain.org/asset/phy03_vid_zstereohangr/

52. 52 Speed of Sound Require medium for transmission Speed varies with –Inertia of molecules –Interaction strength –Temperature Various speeds of sound Internet link: http://hyperphysics.phy- astr.gsu.edu/Hbase/sound/souspe2.ht ml#c1 http://hyperphysics.phy- astr.gsu.edu/Hbase/sound/souspe2.ht ml#c1 Mediumm/sft/s Air (0°C) 3311087 Hydrogen (0°C) 12844213 Water (25°C) 14974911 Lead19606430 Steel594019488 Physics is Life52

53. Physics is Life 53 Describing Sound waves Graphical representation Pure harmonic waves = sines or cosines Wave terminology Wavelength Amplitude Frequency Period Wave propagation speed Wave Properties Review 53

54. Physics is Life 54 Visualization of Sound Waves Sound = spherical wave moving out from source Each crest = wave front Wave motion traced with wave fronts Far from source, wave front becomes planar 54

55. Wave Refraction If there is a change in the characteristics of a medium, waves are bent This occurs because different parts of the wave front travel at different speeds A useful analogy in explaining the refraction of light would be to imagine a marching band as they march from pavement (a fast medium) into mud (a slower medium) The marchers on the side that runs into the mud first will slow down first. This causes the whole band to pivot slightly toward the normal (make a smaller angle from the normal). 55Physics is Life

56. 56 Wave Refraction Wave refraction is the bending of wave fronts upon encountering a boundary due to a change in speedWave refraction –Between two different media –Between different physical circumstances in the same medium Sound travels faster in warm air than cold air! CLICK HERE TO SEE A BEAKER DISAPPEAR USING VEGETABLE OIL AND TWO BEAKERS 56 Why does the pencil appear to be broken?

57. Physics is Life57 Refraction of Waves: An Equation If the wave enters a medium where the wave speed is different, it will be refracted – its wave fronts and rays will change direction. We can calculate the angle of refraction θ 2, which depends on both wave speeds: Known as Snell’s Law If Light goes from fast medium to slow, light bends toward the normal Slow medium to fast, light bends away from the normal 57Physics is Life

58. 58 Refraction of Waves: Speed vs. Frequency The amount of bending and change in velocity of the refracted wave is due to the amount of dispersion corresponding to the wave's frequency, and the refractive index of the material. When light hits the denser material, its frequency remains constant, but its velocity decreases due to the influence of electrons in the denser medium. Constant frequency means that the same number of light waves must pass by in the same amount of time. If the waves are slowing down, wavelength must also decrease to maintain the constant frequency. The waves become more closely spaced, bending toward the normal as if they are being dragged. dispersion frequency Refraction of sound waves influenced the outcome of several Civil War Battles! Acoustician Charles D. Ross has found that refraction of sound caused by temperature and wind gradients may have had a significant impact on the outcome of several Civil War Battles (Gettysburg, Gaines Mill, Fort Donelson, Seven Pines/Fair Oaks, Iuka, Perryville, Chancellorsville, and Five Forks). A summary of his findings are summarized in Echoes, the newsletter of the Acoustical Society of America, and he has a new book Civil War Acoustic Shadows which describes his research in detail.EchoesCivil War Acoustic Shadows

59. Physics is Life59 Sample Problem An earthquake P waves passes a boundary in rock where its velocity increases from 6.5km/s to 8.0km/s. If it strikes this boundary at (  i ) 30 o, what is the angle of refraction? Solution Since sin 30 o = 0.50, using yields sin  2 = (8.0km/s)/(6.5km/s) (0.50) = 0.62 so  2 = 38 o Refraction of Waves: An Equation 59Physics is Life

60. 60 Reflection and Transmission of Waves The law of reflection: the angle of incidence equals the angle of reflection. Light is known to behave in a very predictable manner. If a ray of light could be observed approaching and reflecting off of a flat mirror, then the behavior of the light as it reflects would follow a predictable law known as the law of reflection. 60Physics is Life

61. 61 Reflection and Transmission of Waves Remember...... reflection always makes a V What is the smallest mirror you need to see your whole body? 1/2 your height !

62. Physics is Life 62 Wave Reflection: Sound Wave rebounding off boundary surface Reverberation - sound enhancement from mixing of original and reflected sound waves Echo –Can be distinguished by human ear if time delay between original and reflected sound is greater then 0.1 s –Used in sonar and ultrasonic imaging 62

63. Physics is Life63 Wave Reflection Sample Problem The 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 surface, and 1.80 s later the reflected signal is detected. How deep is the ocean beneath the ship? Solution The time for the wave to travel down and back up is 1.80s. The time for one way is half 1.80 s or 0.900 s. d = vt = (1498m/s)(0.900s) = 1350 m

64. Reflection vs. Absorption Just like light waves, sound waves can be reflected or absorbed Sound waves reflect straight from a smooth, flat surface -There is a clear echo Sound waves are reflected in many directions from a rough, uneven surface -There is no clear echo An echo is formed if the reflected surface is more than 17 meters away from the source.echo To eliminate echoes and excessive reflection of sound waves (reverberation), hard surfaces are covered with soft, irregular shaped absorbing materials. 64Physics is Life64Physics is Life

65. 65 Diffraction of Waves When waves encounter an obstacle, they bend around it, leaving a “shadow region.” This is called diffraction. In this case, water bends around the obstacle. Sound waves also travel freely around obstacles. More Information regarding diffraction: Internet link 65Physics is Life

66. 66 Diffraction of Waves The amount of diffraction depends on the size of the obstacle compared to the wavelength. If the obstacle is much smaller than the wavelength, the wave is barely affected (a). If the object is comparable to, or larger than, the wavelength, diffraction is much more significant (b, c, d). Animation 66Physics is Life

67. 67 Interference of Two Sound Waves of different Frequencies: Beats When two sound waves of different frequency approach your ear, the alternating constructive and destructive interference causes the sound to be alternatively soft and loud - a phenomenon which is called "beating" or producing beats. The beat frequency is equal to the absolute value of the difference in frequency of the two waves. interferencedifference http://www.walter-fendt.de/ph14e/beats.htm 67Physics is Life

68. 68 Beats are caused by the interference of two waves at the same point in space. This plot of the variation of resultant amplitude with time shows the periodic increase and decrease for two sine waves. The image below is the beat pattern produced by a London police whistle, which uses two short pipes to produce a unique and piercing three-note sound.London police whistle Interference of Two Sound Waves of different Frequencies: Beats 68Physics is Life

69. 69 Doppler Effect The Doppler effect The Doppler effect is the change in pitch that occurs when a sound has a velocity relative to the listener. When a sound moves towards the listener the pitch will rise. when going away from the listener the pitch will drop. A well known example is the sound of an ambulance passing by. When an ambulance is coming towards you, the pitch (f=v/ ) of its siren sounds higher to you than it does when the ambulance is at rest. When the ambulance passes by and speeds away from you, the pitch of its siren becomes markedly lower. httphttp://www.colorado.edu/physics/2000/applets/doppler.html 69Physics is Life

70. 70 The Doppler effect is the change in the frequency of waves received by an observer whenever the wave source and the observer are in relative motion toward or away from each other. This applies to all kinds of waves-water waves and light waves, as well as sound waves. Doppler Effect 70Physics is Life How can the Doppler effect be used to explain the concept of an expanding universe?

71. Physics is Life71 Doppler Effect : Sonic Boom Visualization of this phenomena (Click Here) While we're here on the topic of sound and motion, we can also understand sonic booms. Say the car was moving toward you at exactly the speed of sound -- 700 mph or so. The car is blowing its horn. The sound waves generated by the horn cannot go any faster than the speed of sound, so both the car and the horn are coming at you at 700 mph, so all of the sound coming from the car "stacks up." You hear nothing, but you can see the car approaching. At exactly the same moment the car arrives, so does all of its sound and it is LOUD! That is a sonic boom.sonic booms The same phenomenon happens when a boat travels through water faster than waves travel through the water (waves in a lake move at a speed of perhaps 5 mph -- all waves travel through their medium at a fixed speed). The waves that the boat generates "stack up" and form the V-shaped bow wave (wake) that you see behind the boat. The bow wave is really a sonic boom of sorts. It is the stacked-up combination of all of the waves the boat has generated. The wake forms a V shape, and the angle of the V is controlled by the speed of the boat.bow wave

72. Physics is Life72 Summary of Chapter 15 Vibrating objects are sources of waves, which may be either a pulse or continuous. Wavelength: distance between successive crests. Frequency: number of crests that pass a given point per unit time. Amplitude: maximum height of crest. Wave velocity: Resonance: The increase in amplitude of oscillation of an electric or mechanical system exposed to a periodic external force whose frequency is equal to or some multiple of the natural frequency of the system. http://www.regentsprep.org/Regents/physics/phys04/bresonan/default.htm http://www.regentsprep.org/Regents/physics/phys04/bresonan/default.htm 72Physics is Life

73. 73 Summary of Chapter 15 Vibrating objects are sources of waves, which may be either a pulse or continuous. Wavelength: distance between successive crests Frequency: number of crests that pass a given point per unit time Amplitude: maximum height of crest Wave velocity: 73Physics is Life

74. 74 Summary of Chapter 15 Transverse wave: oscillations perpendicular to direction of wave motion. Longitudinal wave: oscillations parallel to direction of wave motion. Angle of reflection is equal to angle of incidence. The Doppler effect is the change in the frequency of waves received by an observer whenever the wave source and the observer are in relative motion toward or away from each other. 74Physics is Life

75. 75 Summary of Chapter 15 When two waves pass through the same region of space, they interfere. Interference may be either constructive or destructive. Standing waves can be produced on a string with both ends fixed. The waves that persist are at the resonant frequencies. Nodes occur where there is no motion; antinodes where the amplitude is maximum. Waves refract when entering a medium of different wave speed, and diffract around obstacles 75Physics is Life

76. 76 Summary of Chapter 15

77. Physics is Life77 Summary of Chapter 15 77Physics is Life

78. 78 WORLD PREMIERE PERFORMACE “I NEED TO STUDY WAVES RIGHT NOW” By J-ROD (RYE HIGH SCHOOL PHYSICS) http://www.youtube.com/watch?v=a xPK08Rh15M&feature=channel