Wave Physics PHYS 2023 Tim Freegarde

Wave propagation 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 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

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

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

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)

Huygens’ wave construction two point sources

Huygens’ wave construction two point sources five point sources

Huygens’ wave construction five point sources 21 point sources

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

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

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

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

Phasors

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

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

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

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

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

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

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

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

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