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Unformatted text preview: 21 Monochromatic waves and phasor notation Recall that we reached the travelingwave dAlembert solutions E , H f ( t z v ) via the superposition of timeshifted and amplitudescaled versions of f ( t ) = cos( t ) , namely the monochromatic waves A cos[ ( t z v )] = A cos( t z ) , with amplitudes A where v = can be called wavenumber in analogy with wavefrequency . T = 2 cos( t ) t 11 Period = 2 cos( z ) z 11 Wavelength As depicted in the margin, monochromatic solutions A cos( t z ) are periodic in position and time, with the wavenumber being essentially a spatialfrequency , the spatial counterpart of . This is an important point that you should try to understand well it has implications for signal processing courses related to images and vision. 1 In general , monochromatic solutions of 1D waveequations ob tained in various branches of science and engineering can all be rep resented in the same format as above in terms of wavefrequency / wavewavenumber pairs and having a ratio v recognized as the wavespeed and specific dispersion relations such as: T = 2 cos( t ) t 11 Period = 2 cos( z ) z 11 Wavelength Dispersion relations between wavefrequency and wavenumber determine the propagation veloc ity v = = f for all types of wave motions.wave motions....
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This note was uploaded on 06/20/2011 for the course ECE 329 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Kim

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