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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. The idea behind Hooke's Law:

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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. The idea behind Hooke's Law: Any object that is initially displaced slightly from a stable equilibrium point will oscillate about its equilibrium position. It will, in general, experience a restoring force that depends on the displacement x from equilibrium.

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

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

  6. Harmonic Motion

  7. 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.

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

  9. Sine Curve

  10. Sine Curve • Pictorial representation of a wave

  11. Simple Tire Swing

  12. Harmonic motion in a Bottle…making a bottle “sing” • Flow of air across bottle top, pulls air out of bottle reducing mass of air in bottle which reduces pressure within bottle. The low pressure pulls air back into bottle causing oscillations. • http://arts.ucsc.edu/ems/music/tech_background/TE-12/teces_12.html

  13. 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.

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

  15. Vibrations and Waves • Waves transmit energy and information. • Sound and Light are examples of waves.

  16. 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

  17. 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.

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

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

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

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

  22. Sine Curve Wavelength  Amplitude A

  23. Crest l Wavelength A A - Amplitude Trough 2. WAVE DESCRIPTION Picture of a Transverse Wave

  24. 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

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

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

  27. Transverse Wave • Particles vibrate perpendicular to the direction the wave travels • Ex. Vibrating string of musical instrument, radio waves

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

  29. Longitudinal Wave • Compression-(similar to crests) – particles close together (high density) • Rarefactions (similar to troughs)- particles spread out or rarefied (low density)

  30. 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

  31. 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

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

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

  34. 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

  35. WAVE MOTION • Energy is transported by particles or waves. A wave is a disturbance transmitted through a medium. • Exception: light does not require a medium. • A disturbance moves through the medium. Causing elements of the medium vibrate. • Example: ripples on water

  36. WAVE MOTION • Medium is disturbed, energy is imparted to it

  37. WAVE SPEED The average speed is defined as

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

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

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

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

  42. 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)

  43. 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

  44. 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

  45. Interference Pattern The pattern formed by superposition of different sets of waves that produce mutual reinforcement in some places and cancellation in others.

  46. Constructive Interference Reinforcement†Maximum In phase displacement

  47. Constructive

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

  49. Destructive- Crests and Troughs overlap CANCELLATION Zero Displacement

  50. Destructive: crests & troughs overlap

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