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 3.00s 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 5.94 m apart. (1)How fast are the waves traveling? (2) What is the amplitude, A, of each wave? (3) What is the angular frequency of the wave? (4) What is the angular number of the wave? (5) What is the displacement of the wave at x = 3.00*10^-2 m and t = 4.30s

Explanation / Answer

We're give the time it takes to move through a half of the period (“from its highest point to its lowest”) so we know that T =3·2s=6s . We're also given the wavelength =5.94m . From the first problem we know that the velocity can be written in terms of the period and wavelength: v= Lameda / T = 5.94/6 = 0.99 m/s --> Answer 2) We're also given twice the amplitude in the same statement quoted in part A, so, A=0.660m/2 =0.33m . --> Answer

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