Vibrations and Waves

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Chapter 14

• Vibrations and Waves

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Simple Harmonic Motion or Periodic Motion Motion
that repeats itself is periodic motion. A
particular kind of periodic motion is known as
simple harmonic motion. When an object is
disturbed from equilibrium, its motion is
probably simple harmonic motion. Here are some
examples of periodic motion that approximate
simple harmonic motion
If the force that restores an object to its
equilibrium position is directly proportional to
the displacement of the object it is Simple
Harmonic Motion
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The amplitude is the maximum distance the mass
moves from its equilibrium position. It moves as
far on one side as it does on the other. The
time that it takes to make one complete
repetition or cycle is called the period of the
motion. We will usually measure the period in
seconds. Frequency is the number of cycles per
second that an oscillator goes through. Frequency
is measured in "hertz" which means cycles per
second. Period and frequency are closely
connected they contain the same information.
T 1/f f 1/T
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Hookes Law
Consider a vertical spring on which we hang a
mass m it will stretch a distance D x because
of the weight of the mass,
                   That stretch is given by
Dxxx m g / k. k is the spring constant of the
spring.
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Now pull the mass down an additional distance x',
The spring is now exerting a force of
Fspring - k x Fspring - k (x'
 x) Fspring - k x' - k  x Fspring - k x' -
mg
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When we add in the force of gravity, we have
Fnet Fspring mg Fnet - k x' - mg mg Fnet
- k x' Now this looks exactly like our
prototypical equation with the displacement x'
now being measured from the new equilibrium
position. This means that everything we have
learned about our prototypical horizontal SHO is
entirely applicable to this more usual vertical
SHO.
PE of a spring PE1/2 kx2
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• Period of motion for a simple pendulum
• The period of a pendulum depends only on its
  length and the acceleration due to gravity
• T 2p (L/g)
• T period in s
• L length in m
• g acceleration due to gravity in m/s2

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Wave Properties

• Transverse Waves direction of vibration is
  perpendicular to the direction of propagation of
  the wave
• Longitudinal Waves direction of vibration is
  the same as the direction of propagation of the
  wave

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Measuring Waves
Frequency number of waves that pass a given
point in a given time Speed of a wave
wavelength x frequency vln or vlf
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Wave Interactions
Reflection bouncing off a barrier
- bending when changing mediums
Diffraction bending around a barrier
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Standing wave
Interference
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Homework

• Pages 396-399
• Numbers 36,40,48,51,52,54,70,73,75,76,96