A fisherman notices that his boat is moving up and down periodically, owing to w

Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.40s  for the boat to travel from its highest point to its lowest, a total distance of 0.680m . The fisherman sees that the wave crests are spaced 6.60m apart.

Part A) How fast are the waves traveling?

Part B) What is the aplitude of each wave?

Part C) If the total vertical distance traveled by the boat were 0.450m, but the other data remained the same, how fast are the waves traveling?

Part D) If the total vertical distance traveled by the boat were 0.450m , but the other data remained the same, what is the amplitude of each wave?

Explanation / Answer

The period of the wave is given T = 2 t

= 2(3.4s)

= 6.8 s

lambda = 6.60 m

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a) speed of the wave is V = f lambda or lambda /T

V = 6.60 / 6.8

= 0.97 m/s

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b) the aplirude of hte wave is A = maximum vertical distance / 2

= 0.680 /2

= 0.34 m

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c) 1.14 m/s

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d)A = d / 2 = 0.450 / 2

= 0.225 m

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