380A OPTI Intermediate Optics Lab 4: Wave Motion
Tom Milster Professor, College of Optical Sciences, University of Arizona [e-mail]
Pendulum
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OPTI380A Lab 4: Wave Motion
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Electromagnetic Waves
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Simple Transverse Waves
One-dimensional wave equation:
!2 Ey !x 2 "
2 1 ! Ey #0 c 2 !t 2
Solution for the real wave traveling in +x direction: E y ( x, t ) y # A0 cos(kx " $t % &) y
if k #
$ . c
y E
E'H
The complete solution involves consideration of the magnetic field. If we take a snapshot in time of the EM wave it may look like:
S=ExH H
z
9/20/2010 OPTI380A Lab 4: Wave Motion
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Simple Transverse Waves
Ey
E00 A wave crest position
x(t ) # vt % x0
x
( # kx " $t
-E -A0 )
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Standing Waves
(Waves traveling in opposite directions)
Ea ( x, t ) # A cos(kx " $t % &a ) Eb ( x, t ) # A cos(" kx " $t % &b )
Addition of the two waves:
& , E ( x, t ) # 2 A cos . kx % * 2 0 &+ , / cos . "$t % / 21 1 0
Square magnitude and irradiance:
E 2 ( x, t ) # A2 21 % cos(2kx % &* ) 3 21 % cos("2$t % &+ )3 I ( x) # cn6 0 E 2 4 x, t 5 # cn60 A2 21 % cos(2kx % &* )3
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Standing Waves
~ 21 % cos(2kx % &* )3 ~ 21 % cos("2$t % &+ )3
7 = )/2
v1 v2
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Ripple Tank
Position Paper Below Tank
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Transmission Line
Wave 1
Wave 2
Result is Standing EM Wave
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Transmission Line
From: http://www.tpub.com/content/neets/14182/css/14182_121.htm
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Transmission Line
From: http://www.tpub.com/content/neets/14182/css/14182_128.htm
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Internet Videos
! Speed of Electrons: http://www.allaboutcircuits.com/vol_2/chpt_14/2.html ! Transmission Line Reflection: http://education.tm.agilent.com/index.cgi?CONTENT_ID=6 ! Reflection from Straight Barrier (Pulse): from Straight Barrier (Pulse): http://www.youtube.com/watch?v=r0088hYFuws&feature=related ! Circular wave reflection ripple tank: http://www.youtube.com/watch?v=-RBpOsgCdxo&feature=related ! Standing wave demo: http://www.youtube.com/watch?v=MT7EpS4OX3k&feature=related ! Waves on a bass instrument: http://www.videosift.com/video/Standing-waves-in-standup-bassguitar-strings
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