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VIBRATIONS AND WAVES

VIBRATIONS AND WAVES. Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law. Harmonic Motion Oscillator.

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VIBRATIONS AND WAVES

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  1. VIBRATIONS AND WAVES

  2. Hooke's Law One of the properties of elasticity is that it takes about twice as much force to stretch a spring twice as far. That linear dependence of displacement upon stretching force is called Hooke's law.

  3. Harmonic Motion Oscillator http://www.kettering.edu/~drussell/Demos/SHO/mass.html

  4. Energy Conversion http://www.kettering.edu/~drussell/Demos/SHO/mass.html

  5. Harmonic Motion

  6. Simple Harmonic Motion (SHM) • Motion that occurs when the restoring force acting on an object is proportional to the object’s displacement from its resting position • Harmonic part if SHM means the motion repeats itself • Objects at the end of springs move in SHM when they are displaced from their rest position and bounce up and down on the spring, or oscillate.

  7. Sine Curve • To and fro vibration motion of swinging pendulum in small arc is called SHM

  8. Sine Curve • Pictorial representation of a wave

  9. Simple Tire Swing

  10. VIBRATION OF A PENDULUM • What does the period (T) depend upon? • Length of the pendulum (l). • Acceleration due to gravity (g). • Period does not depend upon the bob mass.

  11. Pendulum When oscillations are small, the motion is called simple harmonic motion (SHM) and can be described by a simple sine curve.

  12. WAVES • Transfer energy not matter from one place to another • Disturbance that moves through space or through a medium (material)

  13. There are two ways to transmit information/energy in our universe: Particle Motion and Wave Motion Wave Simulation: http://phet.colorado.edu/simulations/sims.php?sim=Wave_Interference

  14. Mechanical Waves • Requires a medium • Ex. Water waves, sound • Two different material objects cannot be in the same place at the same time…however mechanical waves displace matter to transfer energy and thus can be in the same place at the same time.

  15. Electromagnetic Waves • Do not require a medium (can move through empty space, a vacuum) • Ex. Radio waves, light waves, microwaves

  16. Wave Pulse • Single Disturbance http://www.colorado.edu/physics/phys4830/phys4830_fa01/lab/n0911.htm

  17. Wave Train (Continuous Wave) • Series of pulses at regular intervals

  18. Particles vibrate perpendicular to the wave motion Transverse waves can be polarized string musical instruments ripples on water electromagnetic waves e.g. Light waves, x-rays, radio waves TRANSVERSE WAVES

  19. Picture of a Transverse Wave Crest l Wavelength A A - Amplitude Trough

  20. Transverse Wave • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml

  21. Longitudinal Wave • Particles vibrate parallel to the direction of wave travel • Ex. Sound

  22. LONGITUDINAL WAVES Particles vibrate parallel to the motion of the waves Ex: Sound Waves • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml

  23. Rarefactionsare regions of low density. Compressions (condensations) are regions of high density. lis the length of one rarefaction plus one compression Animated comparison of transverse & longitudinal waves: http://members.aol.com/nicholashl/waves/movingwaves.html

  24. Period (T) Time required to make one vibration. • Time required to generate one wave • Time required for the wave to travel one wavelength.

  25. The number of vibrations per unit of time made by the vibrating source. Units -cycles/sec or hertz (Hz) Frequency (f)

  26. Examples of Frequency • What is the frequency of the second hand of a clock? Frequency = 1cycle/60 sec Period = 60 sec • What is the frequency of US Presidential elections? Frequency = 1 election/4 yrs Period = 4 yrs

  27. WAVE SPEED The average speed is defined as

  28. For a wave, if the distance traveled is a wavelength (l), then the time to travel this distance is the period (T). Thus or

  29. is true for all waves. Note: v is determined by the medium. f is dictated by the source.

  30. Surface Water Waves • http://dev.physicslab.org/Document.aspx?doctype=3&filename=WavesSound_IntroductionWaves.xml

  31. Superposition Two or more waves overlapping in some way The overlapping causes interference Animation courtesy of Dr. Dan Russell, Kettering University

  32. Wave Interactions • Because waves are not matter but rather displacement of matter, two waves can occupy the same space at the same time • Combination of two overlapping waves is called superposition (causes interference)

  33. Superposition Principle • Displacement of a medium (material) caused by 2 or more waves is the sum of the displacements of the individual waves at each point • Holds true for all types of waves

  34. Interference • Interference is a characteristic of all waves. • Result of superposition of 2 or more waves • Constructive- (crest meets crest or trough meets trough) amplitudes added • Destructive- (crest meets trough) amplitudes subtract

  35. Constructive Interference Reinforcement†Maximum In phase displacement

  36. Constructive

  37. Constructive Interference • When the crest of one wave overlaps the crest of another

  38. Destructive- Crests and Troughs overlap CANCELLATION Zero Displacement

  39. Destructive: crests & troughs overlap

  40. Interference –Destructive • When the crest of one wave overlaps the trough of another

  41. Standing Waves • When two sets of waves of equal amplitude and wavelength pass through each other in opposite directions, it is possible to create an interference pattern that looks like a wave that is “standing still.”

  42. Standing Wave Incident Wave V Reflected Wave V V Standing Wave V

  43. Standing Waves

  44. Standing Waves • Result of interference and reflection • When 2 sets of waves of equal amplitude and λ pass through each other in opposite directions, the waves are steadily in and out of phase with each other. • Consists of nodes (0 amplitude) and antinodes (max. amplitude) • Wave looks as if it is standing still

  45. Standing Waves • Nodes- point in standing wave that undergoes complete deconstructive interference and is therefore stationary (no vibration) • Antinode- a point in a standing wave (1/2way between 2 nodes) at which the largest amplitude occurs (maximum vibration) Waves on a String: http://phet.colorado.edu/simulations/sims.php?sim=Wave_on_a_String

  46. Standing Waves

  47. Standing Waves • Since the two identical waves travel in opposite directions, the net energy flow is zero; the energy is “standing” in the loops

  48. Standing Wave Harmonics

  49. There is maximum vibration at an antinode. There is no vibration at a node. l

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