Wave Physics PHYS 2023 Tim Freegarde.

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Presentation transcript:

Wave Physics PHYS 2023 Tim Freegarde

Wave Physics WAVE EQUATIONS & SINUSOIDAL SOLUTIONS general wave phenomena wave equations, derivations and solution sinusoidal wave motions complex wave functions WAVE PROPAGATION Huygens’ model of wave propagation interference Fraunhofer diffraction longitudinal waves BEHAVIOUR AT INTERFACES continuity conditions boundary conditions SUPERPOSITIONS linearity and superpositions Fourier series and transforms FURTHER TOPICS waves in three dimensions waves from moving sources operators for waves and oscillations further phenomena and implications http://www.avcanada.ca/albums/displayimage.php?album=topn&cat=3&pos=7

Amplitude and power spectra amplitude spectrum power/intensity spectrum Square wave

Discrete Fourier transform PERIODIC WAVEFUNCTION DISCRETE SPECTRUM COMPLEX SPECTRUM COMPLEX WAVEFUNCTION

Continuous Fourier transform PERIODIC WAVEFUNCTION DISCRETE SPECTRUM NON-PERIODIC WAVEFUNCTION COMPLEX WAVEFUNCTION & SPECTRUM

Fourier transforms Any waveform may be expressed as... a function of time [position]... ...or... a function of frequency [wavenumber] ...where most physical examples are the real part For a single or isolated frequency component, Dirac δ-function

Fourier transform variations* terminology: transform analysis synthesis function periodicity: discrete transform continuous transform integration limits: scale factors: reference functions: signs: * no correlations between rows – ie transform doesn’t mean scale factor = 1 etc.

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Wave Physics for handouts, links and other material, see http://phyweb.phys.soton.ac.uk/quantum/phys2023.php