samp19 - x terms cancel to leave, 9 2 2 1 2 1 2 2 2 = + + +...

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SAMPLE PROBLEM (Class 19) ANS. The distance from source A to a point on the x axis is just x . The distance from point B to a point on the x axis is d x 2 2 + . For destructive interference, the difference between these two distances must be equal to ( n + ½) λ , where n is any integer. Then, if d = 3 , the equation to be solved to find values of x at which there is destructive interference is, ( ) ( ) ( ) 3 2 2 1 2 2 1 2 + - = + + = + + x x n x x n , or 9 2 . If both sides of this equation are squared, The
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Unformatted text preview: x terms cancel to leave, 9 2 2 1 2 1 2 2 2 = + + + x n n ( ) ( ) . Finally, this can be solved for x to give, x n n =-+ + [ ( ) ] ( ) 9 2 1 2 2 1 2 . Examination of this equation shows that x gets smaller as n gets larger, so to find the largest x , we should use the smallest n . Therefore, choose n = 0, and the equation for x becomes, x = (9 ) . Then, x = 8.75...
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