Problem 2

  Two sources are in phase and emit waves that have a wavelength of 0.44 m. Determine whether constructive or destructive interference occurs at a point whose distances from the two sources are as follows: (a) 1.32 and 3.08 m; (b) 2.67 and 3.33 m; (c) 2.20 and 3.74 m; (d) 1.10 and 4.18 m.

SOLUTION: Constructive interference occurs when the path difference $\delta s = path_2 - path_1$ is an even multiple of the half-wavelengths, whereas destructive interference occurs when $\delta s$ is an odd multiple of half-wavelengths.
(a) The path difference 3.08 m - 1.31 m = 1.76 m = 8 half-wavelengths, so the interference is constructive.
(b) Path difference is 0.66 m = 3 half-wavelengths, so destructive.
(c) Path difference = 1.54 m = 7 half-wavelengths, so destructive.
(d) Path difference = 3.08 m = 14 half-wavelengths, so constructive.