Water waves having parallel crests 2.2 cm apart pass throughtwo openings 5.0 cm
ID: 1757437 • Letter: W
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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