The question is incomplete! Complete question along with answer and step by step explanation is provided below.
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 2.60 s for the boat to travel from its highest point to its lowest, a total distance of 0.630 m. The fisherman sees that the wave crests are spaced a horizontal distance of 5.50 m apart.
How much is the wavelength?
How fast are the waves traveling ?
What is the amplitude A of wave?
Given Information:
time = t = 2.60 s
wavelength = λ = 5.50 m
distance = d = 0.630 m
Required Information:
a) wavelength = λ = ?
b) speed = v = ?
c) Amplitude = A = ?
Answer:
a) wavelength = 5.50 m
b) speed = 1.056 m/s
c) Amplitude = 0.315 m
Step-by-step explanation:
a)
It is given that wave crests are spaced a horizontal distance of 5.50 m apart that is basically the wavelength so,
λ = 5.50 m
b)
We know that the speed of the wave is given by
v = λf
where λ is the wavelength and f is the frequency of the wave given by
f = 1/T
Where T is the period of the wave.
Since the it is given that boat takes 2.60 s to travel from its highest point to its lowest that is basically half of the period so one full period is
T = 2*2.60
T = 5.2 s
So the frequency is,
f = 1/5.2
f = 0.192 Hz
Therefore, the speed is
v = λf
v = 5.50*0.192
v = 1.056 m/s
c)
The amplitude of the wave is given by
A = d/2
where d is the distance from the highest point to the lowest, therefore, the amplitude is half of it.
A = 0.630/2
A = 0.315 m