Physics 101: Lecture 21 Waves

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Physics 101 Lecture 21 Waves

• Hour Exam II Average 69.1
• Curve

I remember that this wavelength stuff was the
hardest topic for me in high school, and seeing
as this course is already 3000 times harder than
highschool, well, this might just throw me off
the deep end.
Waves have scared me since I was little and was
dragged into the ocean by one (I am kind of
biased against them). I was hoping that maybe I
would have more luck with these kind of waves but
because I am the most confused I have ever been
after a prelecture the chances are not looking
good. word.
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Waves Overview

• Types
• Speed
• Traveling (harmonic)
• Superposition
• Standing

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Types of Waves
slinky demo
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Slinky Preflight 3

• 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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No, this is not the distance that one coil
moves, it's how fast the wave moves.
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Velocity of Waves Act
slinky-spring demo
A spring and slinky are attached and stretched.
Compare the speed of the wave pulse in the slinky
with the speed of the wave pulse in the
spring. A) vslinky gt vspring B) vslinky
vspring C) vslinky lt vspring
T same. Slinky stretched more, so it has a
smaller mass/length m.
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Traveling (harmonic) Waves
y(x,t) A cos(wtkx)
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
I found relating frequency, period and
wavelength together the hardest thing.
Wave Number k k 2 p / l
Period T 1 / f
y
x
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Period and Velocity

• Period The time T for a point on the wave to
  undergo one complete oscillation.
• T 1 / f

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Traveling Waves Exercise
y(x,t) A cos(wt kx)

• Label axis and tic marks if the graph shows a
  snapshot of the wave
• y(x,t) 2 cos(4t 2x) at x0.
• Recall T 2 p /w

• T 2 p / w
• 2 p/ 4
• p/2
• 1.58

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Preflight 12

• Suppose a traveling wave moves through some
  medium. If the period of the wave is increased,
  what happens to the wavelength of the wave
  assuming the speed of the wave remains the same?
• 1. The wavelength increases
• 2. The wavelength remains the same
• 3. The wavelength decreases

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? v T
Because the wavelength of the wave and the
period are inverse proportional.
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ACT

• 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 ?

(a) 1 GHz (b) 10 GHz (c) 100 GHz
1 GHz 109 cycles/sec
The speed of light is c 3x108 m/s
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ACT Solution

• Recall that v lf.

1 GHz 109 cycles/sec
The speed of light is c 3x108 m/s
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Absorption coefficientof water as a functionof
frequency.
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Interference and Superposition

• When two waves overlap, the amplitudes add.
• Constructive increases amplitude
• Destructive decreases amplitude

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Reflection From Wall

• 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 inverted.
• (Free boundary reflected wave upright)

Reflection demo
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Standing Waves Fixed Endpoints

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

standing wave demo
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Standing Wave Example
f1 fundamental frequency (lowest possible)
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?
v2 T / m m T / v2 m mL T L / v2
82 (0.65) / (428.5)2 2.9 x 10-4 kg
v l f 2 (0.65 m) (329.63 s-1) 428.5
m/s
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Summary

• Wave Types
• Transverse (eg pulse on string, water)
• Longitudinal (sound, slinky)
• Traveling
• 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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