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Class11 - Read Hecht Chapter 2 Bring Hecht textbook with...

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Spherical Harmonic Waves Assume the wave is isotropic: it propagates radially out uniformly in all directions, it does not depend on θ and φ For a constant k this is described by: kr =const , or r =const . (13) For example this could be the wave generated by a point harmonic source spherical symmetry. It is more convenient to use spherical coordinates (Fig. 2.23) to describe this kind of waves. φ cos sin sin cos sin 2 2 2 r z r y r x z y x r = = = + + = (14)
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Spherical Harmonic Waves ( ) ( ) 2 2 2 2 2 v 1 t r r r Ψ = Ψ Spherical harmonic waves : the wave equation: has as solutions the wave function: (15) () t r k i e r A t r t r ω = Ψ = Ψ ) , ( ) , ( r (16) Note : Amplitude is attenuated by a factor 1/r , the further away from the source, the weaker the wave becomes, due to energy conservation.
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Cylindrical Harmonic Waves Cylindrical harmonic waves. Wave has a cylindrical symmetry (rotational symmetry about z axis . Example: wave generated by a line source, or many point sources on a
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Class11 - Read Hecht Chapter 2 Bring Hecht textbook with...

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