Water waves having parallel crests 2.2 cm apart pass throughtwo openings 5.0 cm

Question

Water waves having parallel crests 2.2 cm apart pass throughtwo openings 5.0 cm apart in a board. At a point 2.0 m beyond theboard, at what angle relative to the "straight-through" directionwould there be little or no wave action?
Closest position to the "straight through" line
Next closest position from the "straight through" line
Water waves having parallel crests 2.2 cm apart pass throughtwo openings 5.0 cm apart in a board. At a point 2.0 m beyond theboard, at what angle relative to the "straight-through" directionwould there be little or no wave action?
Closest position to the "straight through" line
Next closest position from the "straight through" line

Explanation / Answer

For destructive interference, the pathdifference is:
           dsin = (m +1/2)           , m = 0,1,2,3,.......       =>sin = [(m + 1/2)(2.2cm)/(5.0cm)] = (m +1/2)(0.44)          ,m= 0,1,2,3,....... The angles for the first three regions ofcomplete destructive interference are            sino = [(m + 1/2)/d] = (0 + 1/2) x (0.44) =0.22,o= 12.71o;            sin1= [(m + 1/2)/d] = (1 + 1/2) x (0.44) =0.66,1 = 41.29o;            sin2= [(m + 1/2)/d] = (2 + 1/2)(0.44) =1.1 =>     no thirdregion. The locations at the end of the tankfrom:            y = Ltan            yo= (2.0 m)tan(12.71o) = (2.0 m) x (0.2255) =0.451 m            y1= (2.0 m)tan(41.49o) = (2.0 m) x (0.8844) =1.77 m => one can stand 0.451 m or 1.77 m away fromthe line perpendicular to the board midway between theopenings.

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