In the figure, sound waves A and B , both of wavelength %u03BB , are initially i

Question

In the figure, sound waves A and B, both of wavelength %u03BB, are initially in phase and traveling rightward, as indicated by the two rays. Wave A is reflected from four surfaces but ends up traveling in its original direction. Wave B ends in that direction after reflecting from two surfaces. Let distance L in the figure be expressed as a multiple q of %u03BB: L = q%u03BB. What are the (a) smallest and (b) second smallest values of q that put A and B exactly out of phase with each other after the reflections?

Explanation / Answer

(a)    from the given we can see that the pathdifference is L    to be out of phase which results indestructive interference the path difference must be    L = (2n + 1) (labda/ 2)    where n = 0, 1, 2, 3, ...........    then we get    L = (lambda / 2), (3 lambda / 2), (5 lambda / 2),.........    the least possiblity is    L = (lambda / 2)    L = q lambda    (lambda / 2) = q lambda    then we get    q = (1 / 2)       = 0.5 (b)    the next possiblity is    L = (3 lambda / 2)    L = q lambda    (3 lambda / 2) = q lambda    then we get    q = (3 / 2)       = 1.5    L = (3 lambda / 2)    L = q lambda    (3 lambda / 2) = q lambda    then we get    q = (3 / 2)       = 1.5

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