problem16_62

University Physics with Modern Physics with Mastering Physics (11th Edition)

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16.62: If the separation of the speakers is denoted , h the condition for destructive interference is λ = - + β x h x 2 2 , where β is an odd multiple of one-half. Adding x to both sides, squaring, cancelling the 2 x term from both sides and solving for x gives λ - λ = 2 2 2 β β h x . Using h f v and = λ from the given data yields 9.01 ( 29 2.71 , m 2 1 = β ( 29 m 27 . 1 , m 2 3 = β ( 29 ( 29 ( 29 2 9 2 7 2 5 m 0.026 and m 53 . 0 , = = = β β β . These are the only allowable values of β that give positive solutions for x . (Negative values of x may be physical, depending on speaker design, but in that case the difference between path lengths is .) 2 2 x h x
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Unformatted text preview: + + b) Repeating the above for integral values of , constructive interference occurs at 4.34 m 0.26 m, 0.86 m, 1.84 m, . Note that these are between, but not midway between, the answers to part (a). c) If , 2 = h there will be destructive interference at speaker , 2 If . h B the path difference can never be as large as 2 . (This is also obtained from the above expression for x , with .) and 2 1 = = x The minimum frequency is then Hz. 86 m) . 4 ( s) m 344 ( 2 = = h v...
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