Waves

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Waves
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Types of Waves
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Period and Velocity
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Slinky Question

• Suppose that a longitudinal wave moves along a
  Slinky at a speed of 5 m/s. Does one coil of the
  slinky move through a distance of five meters in
  one second?
• 1. Yes
• 2. No

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Harmonic Waves
Wavelength The distance ? between identical
points on the wave.
Amplitude The maximum displacement A of a point
on the wave.
Angular Frequency w w 2 p f
Wave Number k k 2 p / l
Recall f v / l
y
x
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Example microwave

• The wavelength of microwaves generated by a
  microwave oven is about 3 cm. At what frequency
  do these waves cause the water molecules in your
  burrito to vibrate ?

The speed of light is c 3x108 m/s
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Interference and Superposition

• When too waves overlap, the amplitudes add.
• Constructive increases amplitude
• l2-l1 m ?
• Destructive decreases amplitude
• l2-l1 (m1/2) ?

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Example two speakers

• Two speakers are separated by a distance of 5m
  and are producing a monotone sound with a
  wavelength of 3m. Other than in the middle,
  where can you stand between the speakers and hear
  constructive interference?

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Example two speakers

• Two speakers are separated by a distance of 5m
  and are producing a monotone sound with a
  wavelength of 3m. Where can you stand between the
  speakers and hear destructive interference?

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Reflection Act

• A slinky is connected to a wall at one end. A
  pulse travels to the right, hits the wall and is
  reflected back to the left. The reflected wave is
• A) Inverted B) Upright
• Fixed boundary reflected wave inverted
• Free boundary reflected wave upright

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Standing Waves Fixed Endpoints

• Fundamental n1
• ln 2L/n
• fn n v / (2L)

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Velocity of Waves on a string
µ mass per unit length of string As µ
increases, v decreases, f decreases (? fixed)
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Example guitar
A guitars E-string has a length of 65 cm and is
stretched to a tension of 82N. If it vibrates
with a fundamental frequency of 329.63 Hz, what
is the mass of the string?
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Summary

• Wave Types
• Transverse (eg pulse on string, water)
• Longitudinal (sound, slinky)
• Harmonic
• y(x,t) A cos(wt kx) or A sin(wt kx)
• Superposition
• Just add amplitudes
• Reflection (fixed point inverts wave)
• Standing Waves (fixed ends)
• ln 2L/n
• fn n v / 2L

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