A fisherman notices that his boat is moving uo and down periodically, owing to waves on the surface of the water. It takes 2.5 s for the boat to travel from its highest point to its lowest, a total distance of 0.62 m. The fisherman sees that the wave crests are spaced 6.0 m apart. (a) How fast are the waves traveling? (b) What is the amplitude of the water? (c) If the total vertical distance traveled by the boat were 0.30 m, but the other date remained the same, how would the answers to parts (a) and (b) be affected?
Part a)
We know the formula for calculating the value of the speed of the wave traveling is:
v = fλ
= λ / T
= (6.0m) / (2.5s + 2.5s)
= (6.0m) / (5.0s) = 1.2m/s
Part c) Amplitude of the water is:
0.62m / 2 = 0.31
Part a)
We know the formula for calculating the value of the speed of the wave traveling is:
v = fλ
= λ / T
= (6.0m) / (2.5s + 2.5s)
= (6.0m) / (5.0s) = 1.2m/s
Part b)
Amplitude of the water is:
0.62m / 2 = 0.31
draw a sketch of the wave crests. You know wavelength, and velocity. You know amplitude. Part c requires some thinking, and we will be happy to critique your thinking.
THe problem is I don't know where to start. I need some help
may I ask how you came up with the value for the wavelength?
the wavelength is given, its the distance between two crests
To find the answers to parts (a), (b), and (c), we can use the formulas related to wave motion.
(a) To find the speed of the waves, we can use the formula:
speed = wavelength / period
The period is the time it takes for the boat to travel from its highest point to its lowest, which is given as 2.5 s.
The wavelength, which is the distance between wave crests, is given as 6.0 m.
Using the formula, we can calculate the speed of the waves:
speed = 6.0 m / 2.5 s = 2.4 m/s
Therefore, the waves are traveling at a speed of 2.4 m/s.
(b) The amplitude of the water is the maximum displacement of the wave from its equilibrium position.
The total distance traveled by the boat from its highest to lowest points is given as 0.62 m. However, the boat only travels half of this distance on each side of the equilibrium position.
Therefore, the amplitude of the wave is:
amplitude = total distance traveled by the boat / 2
amplitude = 0.62 m / 2 = 0.31 m
So, the amplitude of the water is 0.31 m.
(c) If the total vertical distance traveled by the boat were 0.30 m instead of 0.62 m, but the other data remained the same, the answers to parts (a) and (b) would be unaffected.
The speed of the waves is determined by the wavelength and period, which are independent of the total distance traveled by the boat.
Similarly, the amplitude of the water is determined by the total distance traveled by the boat, which is also independent of the other data.
Therefore, changing the total vertical distance traveled by the boat from 0.62 m to 0.30 m would not affect the answers to parts (a) and (b).