In the figure, sound waves A and B, both of wavelength lambda, are initially in

Question

In the figure, sound waves A and B, both of wavelength lambda, 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 lambda: L = q lambda. 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? (a) Number Unit (b) Number Unit click if you would like to show work for this question: open show work

Explanation / Answer

from figure and given conditions, we can write

{3.6q+ 4*(/2)} - {1.2q + 2*(/2)} = p(/2), where p is an odd number or
2.4q + = p(/2) or
4.8q + 2 = p or

4.8q + 2 = p or

q = [(p-2)/4.8]

for p = 3, q = 1/4.8 = 5/24 = 0.2083..........smallest value

for p = 5, q = 3/4.8 = 0.625..........second smallest value

As q is the ratio of same quanity so it does not posses any unit

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