A sound source emits two sinusoidal sound waves, both of wavelength `lambda`, along paths A and B as shown in figure.The sound travelling along path B is reflected from five surfaces as shown and then merges at point Q, producing minimum intensity at that point.The minimum value of d in terms of `lambda` is :

Explanation

Because the two waves emerge from the same source, they must emerge in phase with each other. When they merge at point their phase difference can depend only on the path length difference `Delta L` between the two paths they followed.

To reach Q , the wave following path A travels distance 3d, and the wave following path B travels distance 7d. thus , their path length difference `Delta L` is 4d.
If the waves are to be exactly out of phase at Q, we must have
`(Delta L)/(lamda) = 0.5, 1.5, 2.5 ,...`
Substituting `Delta L = 4d` and solving for d then give us
`d= 1/8 lamda , 3/8 lamda , 5/8 lamda, .............. `
Similarly , if the waves are to be exactly in phase at point Q, we must have
`(Delta L)/(lamda) = 0,1,2,3 ........`
We can eliminate 0 from the list (which that there is no path difference in fig. ) . solving for d, we find
`d = 1/4 lamda ,1/2 lamda, 3/4 lamda` ......... `