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Ocean waves pass through two small openings, 27 m apart, in a breakwater. You're in a boat 69 m from the breakwater and initially midway between the openings, but the water is pretty rough. You row 31m parallel to the breakwater and, for the second time, find yourself in relatively calm water.What is the wavelength of the ocean waves ?
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The figure is below. Initially when in rough water the boat is in position A). The difference in path of incoming waves is zero (or an integer number of wavelengths). Finally the boat is in position B. The difference in path of incoming wave is half wavelength. The length of path of incoming waves in this case is
`p_1 =sqrt(L^2 +(l-d/2)^2) = sqrt(69^2 +(31-27/2)^2) =71.185 m`
`p_2 =sqrt(L^2 +(l+d/2)^2) =sqrt(69^2 +(31+27/2)^2) =82.105 m`
As said above the difference is path is half wavelength.
`lambda = 2*(P_2-P_1) =2*(82.105-71.185) =21.84 m`
Answer: The wavelength of ocean waves is 21.84 m
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