Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.20 s for the boat to travel from its highest point to its lowest, a total distance of 0.680 m . The fisherman sees that the wave crests are spaced 7.00 m apart.

A: How fast are the waves traveling?

B:What is the amplitude of each wave

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

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

Answer 1

Here we have

if time taken by to travel  from its highest point to its lowest is t

than the time period = T = 2t

so here time period = 23.20 = 6.4 seconds

a) velocity =

wavelength = distence between two consecutive crests = 7 m

so velocity = (7)/(6.4) = 1.094 m/s

b) from its highest point to its lowest, the total distance =  0.680 m

so amplitude = 0.680/2 = 0.340 m

so amplitude = 0.340 m

c) here distance of wave is dependent on period of wave and the wavelength so speed of wave will remain unchanged

which is equal to = 1.094 m/s

d) ampitude is half of the distance between two extremes so it will be = 0.500/2 = 0.250 m