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Unformatted text preview: 36.74: a) Recall that the expression for the amplitude of a traveling wave is cos ). ( t kx - Thus each source can be thought of as a traveling wave evaluated at R x = with a maximum amplitude of . E However, each successive source will pick up an extra phase from its respective pathlength to point = sin 2 d . P which is just , 2 the maximum phase, scaled by whatever fraction the path difference, , sin d is of the wavelength, .By adding up the contributions from each source (including the accumulating phase difference) this gives the expression provided. b) ). sin( ) cos( ) ( n t kR i n t kR e n t kR i +- + +- = +- The real part is just cos ). ( n t kR +- So - =- = +- +- = 1 1 ) ( ). cos( e Re N n N n n t kR i n t kR E E (Note: Re means the real part of . . ..) but this is just + +- + +- + +- ) 2 cos( ) cos( ) cos( t kR E t kR E t kR E ). ) 1 ( cos( . .....
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- Spring '08