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Wave Physics

Wave Physics. PHYS 2023. Tim Freegarde. transverse motion of taut string. use physics/mechanics to write partial differential wave equation for system. e-m waves along coaxial cable. shallow-water waves. Wave propagation. flexure waves. string with friction. travelling wave:.

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Wave Physics

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  1. Wave Physics PHYS 2023 Tim Freegarde

  2. transverse motion of taut string use physics/mechanics to write partial differential wave equation for system • e-m waves along coaxial cable • shallow-water waves Wave propagation • flexure waves • string with friction • travelling wave: • general form • sinusoidal insert generic trial form of solution • complex exponential • damped • standing wave • soliton • speed of propagation find parameter values for which trial form is a solution • dispersion relation • string motion from initial conditions

  3. today’s lecture: • Huygens’ construction Wave propagation in changing media • gradual change: • refraction • refraction; continuity conditions • obstacles: • interface between media: • 1-D: boundary conditions • 2/3-D: diffraction

  4. waves are Wave propagation • 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

  5. wavefronts propagate from initial disturbance in all directions Huygens’ wave construction • 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)

  6. two point sources Huygens’ wave construction

  7. five point sources • two point sources Huygens’ wave construction

  8. 21 point sources • five point sources Huygens’ wave construction

  9. propagation from a point source Huygens’ wave construction Christiaan Huygens (1629-1695)

  10. reflection at a plane surface Huygens’ wave construction Christiaan Huygens (1629-1695)

  11. refraction at a plane surface Huygens’ wave construction Christiaan Huygens (1629-1695)

  12. refraction at a plane surface Huygens’ wave construction Christiaan Huygens (1629-1695)

  13. Phasors

  14. Huygens’ wave construction • Fresnel integral • phasors shorter / rotate more quickly at distance to give spiral

  15. a b x x 0 L S S Fermat’s principle of least time B C A P P • refraction at a plane surface Pierre de Fermat (1601-1665)

  16. a b x x 0 L Pierre de Fermat (1601-1665) S S • light rays follow the path of least time between two points Fermat’s principle of least time P P • refraction at a plane surface

  17. a b x x 0 L Willebrord Snel van Royen (Leiden, 1580-1626) S S • light rays follow the path of least time between two points Snell’s law of refraction P P • refraction at a plane surface

  18. mirages by refraction in the atmosphere Huygens’ wave construction Christiaan Huygens (1629-1695)

  19. ocean waves parallel to shore Huygens’ wave construction Christiaan Huygens (1629-1695)

  20. http://www.uwgb.edu/dutchs/EarthSC202Slides/COASSLID.HTM Huygens’ wave construction • ocean waves parallel to shore Christiaan Huygens (1629-1695)

  21. http://geographyfieldwork.com/WaveRefraction.htm Huygens’ wave construction Christiaan Huygens (1629-1695)

  22. http://www.dorsetphotos.co.uk http://www.smccd.edu/accounts/bramalln/documents/waterwaves.pdf Christiaan Huygens (1629-1695) Google Earth Huygens’ wave construction

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