Wave Physics
PHYS 2023
Tim Freegarde
Wave propagation
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•
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transverse motion of taut string
e-m waves along coaxial cable
shallow-water waves
flexure waves
string with friction
• travelling wave:
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general form
sinusoidal
complex exponential
damped
use physics/mechanics to
write partial differential wave
equation for system
insert generic trial form of
solution
• standing wave
• soliton
• speed of propagation
• dispersion relation
• string motion from initial conditions
find parameter values for
which trial form is a solution
2
Wave propagation in changing media
• today’s lecture:
• Huygens’ construction
• gradual change:
• refraction
• interface between media:
• refraction; continuity conditions
• obstacles:
• 1-D: boundary conditions
• 2/3-D: diffraction
3
Wave propagation
waves are
• collective bulk disturbances, in which
• motion is a delayed response
• to neighbouring motions
when propagation follows multiple routes
• the amplitudes are added
• waves propagate via all possible routes
4
Huygens’ wave construction
• wavefronts propagate from initial disturbance
in all directions
• each point on the wavefront acts as a
secondary source
• further wavefronts propagate from the
secondary sources in the same fashion
• where wavefronts coincide (strong constructive
interference), a new wavefront is formed
Christiaan Huygens (1629-1695)
5
Huygens’ wave construction
• two point sources
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Huygens’ wave construction
• two
five point sources
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Huygens’ wave construction
• five
21 point
pointsources
sources
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Huygens’ wave construction
• propagation from a point source
Christiaan Huygens (1629-1695)
9
Huygens’ wave construction
• reflection at a plane surface
Christiaan Huygens (1629-1695)
10
Huygens’ wave construction
• refraction at a plane surface
Christiaan Huygens (1629-1695)
11
Huygens’ wave construction
• refraction at a plane surface
Christiaan Huygens (1629-1695)
12
Phasors
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Huygens’ wave construction
• Fresnel integral
• phasors shorter / rotate more quickly
at distance to give spiral
14
Fermat’s principle of least time
S
S
A
a
B
C
P
b
P
0
x
L
x
• refraction at a plane surface
Pierre de Fermat (1601-1665)
15
Fermat’s principle of least time
S
S
a
P
• light rays follow the path of least time
between two points
b
P
0
x
L
x
• refraction at a plane surface
Pierre de Fermat (1601-1665)
16
Snell’s law of refraction
S
S
a
P
• light rays follow the path of least time
between two points
b
P
0
x
L
• refraction at a plane surface
x
Willebrord Snel van Royen
(Leiden, 1580-1626)
17
Huygens’ wave construction
• mirages by refraction in the atmosphere
Christiaan Huygens (1629-1695)
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Huygens’ wave construction
• ocean waves parallel to shore
Christiaan Huygens (1629-1695)
19
Huygens’ wave construction
http://www.uwgb.edu/dutchs/EarthSC202Slides/COASSLID.HTM
• ocean waves parallel to shore
Christiaan Huygens (1629-1695)
20
Huygens’ wave construction
Christiaan Huygens (1629-1695)
http://geographyfieldwork.com/WaveRefraction.htm
21
Huygens’ wave construction
http://www.dorsetphotos.co.uk
http://www.smccd.edu/accounts/bramalln/documents/waterwaves.pdf
Christiaan Huygens (1629-1695)
Google Earth
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