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Wave Physics

Wave Physics. Tim Freegarde. Longitudinal waves. 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. rest. displaced. x. x+ δ x. Longitudinal waves. P. Q.

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Wave Physics

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  1. Wave Physics Tim Freegarde

  2. Longitudinal waves 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

  3. rest displaced x x+δx Longitudinal waves P Q use physics/mechanics to write partial differential wave equation for system O R ξ ξ+δξ insert generic trial form of solution O R T(x) find parameter values for which trial form is a solution P′ Q′

  4. Speed of sound • metals 4 000 m s-1 • air at sea level 330 m s-1 • helium 970 m s-1 • water 1 500 m s-1

  5. x x+δx Thermal waves (diffusion) 1 2 use physics/mechanics to write partial differential wave equation for system W insert generic trial form of solution W1 W2 find parameter values for which trial form is a solution

  6. y W W δx x-δx x x+δx x A frayed guitar string

  7. combine forward and reflected waves to give total fields for each region Reflection at an interface apply continuity conditions for separate components hence derive fractional transmission and reflection

  8. combine forward and reflected waves to give total fields for each region Reflection at an interface apply continuity conditions for separate components hence derive fractional transmission and reflection

  9. Anti-reflection coatings • dielectric coatings reduce reflections at surfaces of lens elements www.sciencebuddies.org

  10. Anti-reflection coatings • quarter-wave structures at radar wavelengths (cm), together with orientation of surfaces, reduces radar reflectivity of Stealth aircraft www.airforcetechnology.com

  11. Snell’s law: Total internal reflection

  12. Snell’s law: Total internal reflection

  13. Total internal reflection

  14. Evanescent waves

  15. Frustrated total internal reflection (tunnelling)

  16. first six harmonics lie on major chord Open organ pipe J S Bach Toccata & Fugue in D minor BWV565

  17. ξ n′ = 1 x 0 L n′ = 3 n′ = 2 • even harmonics are absent Stopped organ pipe

  18. The bell • cyclic boundary conditions

  19. Loudspeaker design • Bose ‘acoustic waveguide’ www.bose.com

  20. www.nxtsound.com www.popularmechanics.com Loudspeaker design • NXT distributed mode loudspeaker

  21. x Plucked guitar string

  22. The Fender Stratocaster • scale length 25½” (648mm) • three sets of pick-ups www.fender.com

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