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 a time of 2.90 s for the boat to travel from its highest point to its lowest, a total distance of 0.660 m. The fisherman sees that the wave crests are spaced a horizontal distance of 6.13 m apart.

A) How fast are the waves traveling?

B) What is the amplitude A of each wave?

C) What is the angular frequency of the wave?

D) What is the angular wave number of the wave?

E) What is the displacement of the wave at x = 0.200 m, and t = 8.30 s?

Explanation / Answer

a) speed of wave = 6.13/2.92.113 m/s

b) amplitude of wave = 0.66/2 = 0.33 m

c) angular frequency = 2*pi/2.9 = 2.166 s-1

d)angular wave number = 2*pi/6.13 = 1.025 m-1

e)displacement at given conditions = 0.289 m

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