Wave Physics PHYS 2023 Tim Freegarde. 2 Wave propagation use physics/mechanics to write partial...
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Transcript of Wave Physics PHYS 2023 Tim Freegarde. 2 Wave propagation use physics/mechanics to write partial...
Wave PhysicsPHYS 2023
Tim Freegarde
2
Wave propagation
use physics/mechanics to write partial differential
wave equation for system
insert generic trial form of solution
find parameter values for which trial form is a
solution
• transverse motion of taut string
• travelling wave:
• e-m waves along coaxial cable• shallow-water waves
• flexure waves• string with friction
• general form• sinusoidal• complex
exponential
• standing wave
• damped
• soliton
• speed of propagation• dispersion relation• string motion from initial conditions
3
Wave propagation in changing media
• Huygens’ construction
• gradual change: • refraction
• refraction; continuity conditions
• obstacles: • 1-D: boundary conditions
• 2/3-D: diffraction
• today’s lecture:
• interface between media:
4
Wave propagation
waves are• collective bulk disturbances, in
which• motion is a delayed response• to neighbouring motions
• the amplitudes are added
when propagation follows multiple routes
• waves propagate via all possible routes
5
Huygens’ wave construction
• wavefronts propagate from initial disturbance in all directions
Christiaan Huygens (1629-1695)
• 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
6
Huygens’ wave construction
• two point sources
7
Huygens’ wave construction
• five point sources• two point sources
8
Huygens’ wave construction
• 21 point sources• five point sources
9
Huygens’ wave construction
• propagation from a point sourceChristiaan Huygens (1629-1695)
10
Huygens’ wave construction
• reflection at a plane surfaceChristiaan Huygens (1629-1695)
11
Huygens’ wave construction
• refraction at a plane surfaceChristiaan Huygens (1629-1695)
12
Huygens’ wave construction
• refraction at a plane surfaceChristiaan Huygens (1629-1695)
13
Phasors
14
Huygens’ wave construction
• Fresnel integral• phasors shorter / rotate more
quickly at distance to give spiral
15
Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
A B C
S
P
S
P
x
16
Fermat’s principle of least time
• refraction at a plane surfacePierre de Fermat (1601-1665)
x0 L
a
b
S
P
x
• light rays follow the path of least time between two points
S
P
17
Snell’s law of refraction
• refraction at a plane surface
x0 L
a
b
S
P
x
• light rays follow the path of least time between two points
Willebrord Snel van Royen(Leiden, 1580-1626)
S
P
18
Huygens’ wave construction
• mirages by refraction in the atmosphereChristiaan Huygens (1629-1695)
19
Huygens’ wave construction
Christiaan Huygens (1629-1695)
• ocean waves parallel to shore
20
Huygens’ wave construction
Christiaan Huygens (1629-1695)
• ocean waves parallel to shorehttp://www.uwgb.edu/dutchs/EarthSC202Slides/
COASSLID.HTM
21
Huygens’ wave construction
Christiaan Huygens (1629-1695)
http://geographyfieldwork.com/WaveRefraction.htm
22
Huygens’ wave construction
Christiaan Huygens (1629-1695)
http://www.smccd.edu/accounts/bramalln/documents/waterwaves.pdf
http://www.dorsetphotos.co.uk
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