Wave Physics PHYS 2023 Tim Freegarde

Fourier transforms Uses of Fourier transforms: Reveal which frequencies/wavenumbers are present identification or analysis system performance definition Energy/power/intensity calculations orthogonality means component powers may simply be added Propagation in dispersive systems determine propagation of individual components, and add group velocity Fraunhofer diffraction Bandwidth theorem / Heisenburg uncertainty principle Convolution theorem

3 3 Beating TWO DIFFERENT FREQUENCIES

4 4 Bandwidth theorem

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7 bandwidth theorem: uncertainty= standard deviation in = root mean square deviation for conjugate variables, (time, frequency): (position, wavenumber): equality holds for Gaussian pulses

8 Bandwidth theorem bandwidth theorem: uncertainty= standard deviation in = root mean square deviation for conjugate variables, (time, frequency): (position, wavenumber): equality holds for Gaussian pulses last year’s results

9 Bandwidth theorem bandwidth theorem: uncertainty= standard deviation in = root mean square deviation for conjugate variables, (time, frequency): (position, wavenumber): equality holds for Gaussian pulses this year’s results!

10 Sound waves wave equation: where the elasticity ratio of specific heats ambient pressure wave velocity: air helium SF kg m -3 m s -1