Wave Physics PHYS2023

Wave PhysicsPHYS 2023

Tim Freegarde12Thermal waves (diffusion)xx+xuse physics/mechanics to write partial differential wave equation for systeminsert generic trial form of solutionfind parameter values for which trial form is a solution12W1W2W2

3Traffic wavesY Sugiyama et al., N J Phys 10, 033001 (2008)22 vehicles on 230 m circumferencerequested to cruise at 30 kmhjam propagates backwards at ~20 kmh3

4Sumatra-Andaman earthquake 2004Tsunami Inundation Mapping EffortsNOAA/PMEL - UW/JISAO26 DEC 2004 04:15Z===================MAGNITUDE 9.1 EARTHQUAKE ALONGINDIA-BURMA SUBDUCTION ZONE.1200KM FAULT LEAVING KM-WIDERIDGES AND TROUGHS.30 CUBIC-KM WATER DISPLACED.+2HRS WAVE HEIGHT 0.6M+3HRS WAVE HEIGHT 0.4MNOAA SATELLITE RADAR REPORTSFROM: UN ENVOY SUMATRATO: CHIEF SCI ADVISOR LONDONPLS ADVISE ++ UTMOST URGENCY ++4

5Sumatra-Andaman earthquake 2004Uwe Dedering / Wikipedia Commons26 DEC 2004 04:15Z===================MAGNITUDE 9.1 EARTHQUAKE ALONGINDIA-BURMA SUBDUCTION ZONE.1200KM FAULT LEAVING KM-WIDERIDGES AND TROUGHS.30 CUBIC-KM WATER DISPLACED.+2HRS WAVE HEIGHT 0.6M+3HRS WAVE HEIGHT 0.4MNOAA SATELLITE RADAR REPORTSFROM: UN ENVOY SUMATRATO: CHIEF SCI ADVISOR LONDONPLS ADVISE ++ UTMOST URGENCY ++MaldivesSeychellesMauritius/Reunion5

6Sumatra-Andaman earthquake 2004Uwe Dedering / Wikipedia CommonsMaldivesSeychellesMauritius/ReunionUN Office for the Coordination of Human Affairs6

7Sumatra-Andaman earthquake 2004NOAA radar was experimentaldata analysis and wave simulation were not possible until days later275,000 people perishedUN Office for the Coordination of Human Affairs

Tsunami Inundation Mapping EffortsNOAA/PMEL - UW/JISAO78

Wave PhysicsWAVE EQUATIONS & SINUSOIDAL SOLUTIONSwave equations, derivations and solution

sinusoidal wave motions

complex wave functions

WAVE PROPAGATIONHuygens model of wave propagation

interference

general wave phenomena

Fraunhofer diffraction

longitudinal waves

BEHAVIOUR AT INTERFACEScontinuity conditionsboundary conditions

SUPERPOSITIONSlinearity and superpositions

Fourier series and transforms

FURTHER TOPICSwaves from moving sources

operators for waves and oscillations

waves in three dimensions

http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7further phenomena and implications

89Wave propagationuse physics/mechanics to write partial differential wave equation for systeminsert generic trial form of solutionfind parameter values for which trial form is a solutiontransverse motion of taut stringtravelling wave:e-m waves along coaxial cableshallow-water wavesflexure wavesstring with frictiongeneral formsinusoidalcomplex exponentialstanding wavedampedsolitonspeed of propagationdispersion relationHuygens reflection, refraction and diffractionreflection and transmission at interfacesstring motion from initial conditions910A frayed guitar stringxxx+xx-x

WWx

1011Reflection at an interfacecombine forward and reflected waves to give total fields for each regionapply continuity conditions for separate componentshence derive fractional transmission and reflection

1112Continuity conditionsfor a boundary at between regions A and B:

transverse waves on a string:electromagnetic waves:non-normal incidence:sound waves:thermal waves:

1213Significance of continuity conditionsvarious derivations and formstypically:one condition derived from balance of forcesconservation of momentumthe two conditions combinedconservation of energyTransverse waves on a string

energy density: power:

where1314Energy of waves on a stringxxh(x)xvy14