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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 ϖ- 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 = λ sin 2 θ π φ d . P which is just , 2 π the maximum phase, scaled by whatever fraction the path difference, , sin θ d is of the wavelength, λ.By adding up the contributions from each source (including the accumulating phase difference) this gives the expression provided. b) ). sin( ) cos( ) ( φ ϖ φ ϖ φ ϖ n t kR i n t kR e n t kR i +- + +- = +- The real part is just cos ). ( φ ϖ n t kR +- So ∑ ∑- =- = +- +- = 1 1 ) ( ). cos( e Re N n N n n ωt kR i n ωt kR E E φ φ (Note: Re means “the real part of . . ..”) but this is just + +- + +- + +- ) 2 cos( ) cos( ) cos( φ ϖ φ ϖ φ ϖ t kR E t kR E t kR E ). ) 1 ( cos( . .....
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This note was uploaded on 01/24/2010 for the course PHYS 208 taught by Professor Ross during the Spring '08 term at Texas A&M.
- Spring '08