Question

A fisherman notices that his boat is moving up and down periodically without any horizontal motion, owing to waves on the surface of the water. It takes a time of 2.90s for the boat to travel from its highest point to its lowest, a total distance of 0.630m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.60m apart.
1. How much is the wavelength?
express your answers in 3 sig. fig.
2.Find the period of the wave.
3 sig. fig.
3.How fast are the waves traveling?
Express the speed v in meters per second using three significant figures.
4. What is the amplitude A of each wave?
Express your answer in meters using three significant figures.

Answer 1

Answer:

1.  λ = 5.60 m , 2.  T = 5.80 s  3.  v = 0.966 m/s   4.  A = 0.315 m

Explanation:

1. The definition of wavelength is the distance between two consecutive maximums or minimums, so that the wave is repeated, in this case they give us the distance between two consecutive maximums, therefore

    λ = 5.60 m

2. the period is the time it takes for the wave to start repeating itself, going through the same point. They give time to go from the highest point to the lowest point, which is the time for half a wavelength, so the time for a wavelength is

     T = 2 t

     T = 2 2.90

     T = 5.80 s

3. For all waves the speed is the product of the wavelength by the frequency and the frequency is the inverse of the period

    v = λ f

    f = 1 / T

   v =  λ / T

   v = 5.60 / 5.80

   v = 0.966 m / s

4. The amplitude of the wave is the value of the zero displacement point to the maximum displacement point, give the value between the maximum and minimum displacement

     A = d / 2

     A = 0.63 / 2

     A = 0.315 m