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 3.00 s for the boat to travel from its highest point to its lowest, a total distance of 0.700 m . The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.

Required:
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 , 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 , but the other data remained the same, what is the amplitude of each wave?

Answer 1

a) v = 0.9167 m / s, b) A = 0.350 m, c) v = 0.9167 m / s, d) A = 0.250 m

Step-by-step explanation:

a) to find the velocity of the wave let us use the relation

v = λ f

the wavelength is the length that is needed for a complete wave, in this case x = 5.50 m corresponds to a wavelength

λ = x

λ = x

the period is the time for the wave to repeat itself, in this case t = 3.00 s corresponds to half a period

T / 2 = t

T = 2t

period and frequency are related

f = 1 / T

f = 1 / 2t

we substitute

v = x / 2t

v = 5.50 / 2 3

v = 0.9167 m / s

b) the amplitude is the distance from a maximum to zero

2A = y

A = y / 2

A = 0.700 / 2

A = 0.350 m

c) The horizontal speed of the traveling wave (waves) is independent of the vertical oscillation of the particles, therefore the speed is the same

v = 0.9167 m / s

d) the amplitude is

A = 0.500 / 2

A = 0.250 m