Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.80 for the boat to travel from its highest point to its lowest, a total distance of 0.620 . The fisherman sees that the wave crests are spaced 6.40 apart.
How fast are the waves traveling? in m/s

What is the amplitude of each wave? in m

If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, how fast are the waves traveling ? in m/s

If the total vertical distance traveled by the boat were 0.500 , but the other data remained the same, what is the amplitude of each wave? in m

Answer 1

Answer:

a)1.14

b)0.31

c)1.14

d)0.25

Explanation:

Assume wave travels in a harmonic motion. This means if it takes 2.8 for the boat to travel from highest to lowest point, then it'd take 2.8*2 = 5.6 for the boat to travel in 1 period (from highest point to lowest point then back to highest point again).

a)As the wave crest is 6.4 apart. Then it's speed is

v = s/t = 6.4/5.6 = 1.14

b) The amplitude would be half of the vertical distance traveled by the boat, which is

A = 0.62 / 2 = 0.31

c) As the distance between the crest and the time it takes for the boat to travel vertically is unchanged, then the wave speed would stay the same:

v = 1.14

d) The amplitude would again be half of the vertical distance

A = 0.5 / 2 = 0.25