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# Waves and Vibrations

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### Waves and Vibrations

1. 1. 1Waves and VibrationsPhysics:1/29/2013
2. 2. 1. Two ways to get in touch with a friend in adistant city are to write a letter and to useTelephone.2. The first choice (the letter) involves aconcept of particle.3. A material object moves from one point toanother, carrying with it information andenergy.4. The second choice (the Telephone)involves the concept of wave.Wave motion
3. 3. 5. In a wave, information and energy move fromone point to another but no material object makesthat journey.6. In your Telephone call, a sound carries yourmessage from your vocal cords to the Telephonealthough the message is passed nothing that youhave touched reaches your friend7. In Telephone an electromagnetic wave takesover, passing along a copper wire or an optical fiberare through the atmosphere, possibly by way of acommunications satellite.8. Particle and wave are two great concepts inclassical physics.
4. 4. What is a wave?A wave is a disturbance in a medium that travelsoutward from its source.It travels from one place to another by means ofa medium, but the medium itself is nottransported.All material media- solids, liquids, and gases-can carry energy and information by means ofwaves.There are many types of wave.All types of waves use similar mathematicaldescriptions.
6. 6. 6What is a wave?a wave is a disturbance that travelsthrough a medium from one location toanother.a wave is the motion of a disturbance
7. 7. 7Slinky WaveLet’s use a slinky wave as an example.When the slinky is stretched from end toend and is held at rest, it assumes anatural position known as theequilibrium or rest position.To introduce a wave here we must firstcreate a disturbance.We must move a particle away from itsrest position.
8. 8. 8Slinky WaveOne way to do this is to jerk the slinky forwardthe beginning of the slinky moves away from itsequilibrium position and then back.the disturbance continues down the slinky.this disturbance that moves down the slinky iscalled a pulse.if we keep “pulsing” the slinky back and forth,we could get a repeating disturbance.
9. 9. 9Slinky WaveThis disturbance would look something like thisThis type of wave is called a LONGITUDINAL wave.The pulse is transferred through the medium of theslinky, but the slinky itself does not actually move.It just displaces from its rest position and thenreturns to it.So what really is being transferred?
10. 10. 10Slinky WaveEnergy is being transferred.The metal of the slinky is the MEDIUM in thattransfers the energy pulse of the wave.The medium ends up in the same place as itstarted … it just gets disturbed and then returnsto it rest position.The same can be seen with a stadium wave.
11. 11. 11Longitudinal WaveThe wave we see here is a longitudinal wave.The medium particles vibrate parallel to themotion of the pulse.This is the same type of wave that we use totransfer sound.Can you figure out how??
12. 12. 12Transverse wavesA second type of wave is a transversewave.We said in a longitudinal wave the pulsetravels in a direction parallel to thedisturbance.In a transverse wave the pulse travelsperpendicular to the disturbance.
13. 13. 13Transverse WavesThe differences between the two can beseen
14. 14. 14Transverse WavesTransverse waves occur when we wigglethe slinky back and forth.They also occur when the sourcedisturbance follows a periodic motion.A spring or a pendulum can accomplishthis.The wave formed here is a SINE wave.
15. 15. 15Anatomy of a WaveNow we can begin to describe theanatomy of our waves.We will use a transverse wave to describethis since it is easier to see the pieces.
16. 16. 16Anatomy of a WaveIn our wave here the dashed line represents theequilibrium position.Once the medium is disturbed, it moves awayfrom this position and then returns to it
17. 17. 17Anatomy of a WaveThe points A and F are called the CRESTSof the wave.This is the point where the wave exhibitsthe maximum amount of positive orupwards displacementcrest
18. 18. 18Anatomy of a WaveThe points D and I are called theTROUGHS of the wave.These are the points where the waveexhibits its maximum negative ordownward displacement.trough
19. 19. 19Anatomy of a WaveThe distance between the dashed line andpoint A is called the Amplitude of the wave.This is the maximum displacement that thewave moves away from its equilibrium.Amplitude
20. 20. 20Anatomy of a WaveThe distance between two consecutive similarpoints (in this case two crests) is called thewavelength.This is the length of the wave pulse.Between what other points is can a wavelength bemeasured?wavelength
21. 21. 21Anatomy of a WaveWhat else can we determine?We know that things that repeat have afrequency and a period. How could wefind a frequency and a period of awave?
22. 22. 22Wave frequencyWe know that frequency measure howoften something happens over a certainamount of time.We can measure how many times a pulsepasses a fixed point over a given amountof time, and this will give us thefrequency.
23. 23. 23Wave frequencySuppose I wiggle a slinky back and forth,and count that 6 waves pass a point in 2seconds. What would the frequency be?3 cycles / second3 Hzwe use the term Hertz (Hz) to stand forcycles per second.
24. 24. 24Wave PeriodThe period describes the same thing as itdid with a pendulum.It is the time it takes for one cycle tocomplete.It also is the reciprocal of the frequency.T = 1 / ff = 1 / T
25. 25. 25Wave SpeedWe can use what we know to determinehow fast a wave is moving.What is the formula for velocity?velocity = distance / timeWhat distance do we know about a wavewavelengthand what time do we knowperiod
26. 26. 26Wave Speedso if we plug these in we getvelocity =length of pulse /time for pulse to move pass a fixed pointv = λ / Twe will use the symbol λ to representwavelength
27. 27. 27Wave Speedv = λ / Tbut what does T equalT = 1 / fso we can also writev = f λvelocity = frequency * wavelengthThis is known as the wave equation.
28. 28. 28Wave BehaviorNow we know all about waves.How to describe them, measure them andanalyze them.But how do they interact?
29. 29. 29Wave BehaviorWe know that waves travel throughmediums.But what happens when that medium runsout?
30. 30. 30Boundary BehaviorThe behavior of a wave when it reachesthe end of its medium is called the wave’sBOUNDARY BEHAVIOR.When one medium ends and anotherbegins, that is called a boundary.
31. 31. 31Fixed EndOne type of boundary that a wave mayencounter is that it may be attached to afixed end.In this case, the end of the medium willnot be able to move.What is going to happen if a wave pulsegoes down this string and encounters thefixed end?
32. 32. 32Fixed EndHere the incident pulse is an upwardpulse.The reflected pulse is upside-down. It isinverted.The reflected pulse has the same speed,wavelength, and amplitude as theincident pulse.
33. 33. 33Fixed End Animation
34. 34. 34Free EndAnother boundary type is when a wave’smedium is attached to a stationary objectas a free end.In this situation, the end of the medium isallowed to slide up and down.What would happen in this case?
35. 35. 35Free EndHere the reflected pulse is not inverted.It is identical to the incident pulse, exceptit is moving in the opposite direction.The speed, wavelength, and amplitudeare the same as the incident pulse.
36. 36. 36Free End Animation
37. 37. 37Change in MediumOur third boundary condition is when themedium of a wave changes.Think of a thin rope attached to a thinrope. The point where the two ropes areattached is the boundary.At this point, a wave pulse will transferfrom one medium to another.What will happen here?
38. 38. 38Change 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 themore dense medium, and part is reflected.The transmitted pulse is upright, while thereflected pulse is inverted.
39. 39. 39Change in MediumThe speed and wavelength of thereflected wave remain the same, but theamplitude decreases.The speed, wavelength, and amplitude ofthe transmitted pulse are all smaller thanin the incident pulse.
40. 40. 40Change in Medium Animation
41. 41. 41Wave InteractionAll we have left to discover is how wavesinteract with each other.When two waves meet while travelingalong the same medium it is calledINTERFERENCE.
42. 42. 42Constructive InterferenceLet’s consider two waves moving towardseach other, both having a positiveupward amplitude.What will happen when they meet?
43. 43. 43Constructive InterferenceThey will ADD together to produce agreater amplitude.This is known as CONSTRUCTIVEINTERFERENCE.
44. 44. 44Destructive InterferenceNow let’s consider the opposite, twowaves moving towards each other, onehaving a positive (upward) and one anegative (downward) amplitude.What will happen when they meet?
45. 45. 45Destructive InterferenceThis time when they add together theywill produce a smaller amplitude.This is know as DESTRUCTIVEINTERFERENCE.
46. 46. 46Check Your Understanding Which points will produce constructive interferenceand which will produce destructive interference? ConstructiveG, J, M, N DestructiveH, I, K, L, O