A fisherman notices that his boat is moving up and down periodically, owing to w

Question

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.77s for the boat to travel from its highest point to its lowest, a total distance of 0.644m . The fisherman sees that the wave crests are spaced 6.95m 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 0.372m , but the other data remained the same, how fast are the waves traveling ?

d) If the total vertical distance traveled by the boat were 0.372m , but the other data remained the same, what is the amplitude of each wave?

Explanation / Answer

1.from the data given:
Time for wave to travel from highest point to lowest = 2.77 sec.
This corresponds to half of one wavelength.
Therefore, time for one whole wavelength = 5.54 sec.

The wave crests are spaced 6.95 m. apart.
This corresponds to the distance from one peak to the next peak of the waves.
By definition, this is one whole wavelength.
Hence, one wavelength = 6.95 m.

Since the speed of the wave = distance / time, we have speed = 6.95 m. divided by 5.54 sec.
And that is 1.255 m / sec.; the speed of the wave in a horizontal direction.

2.As for the amplitude of the wave, the highest point of the wave to its lowest point is 0.644 m (The boat always sits on the wave - I assume it isn't sinking!)
This distance corresponds to the peak - peak vertical displacement of the wave.
Therefore, the amplitude is half of this, i.e. 0.322 m.

If the total vertical distance traveled by the boat were 0.372m, but the other data remained the same, how fast are the waves traveling? & what is the amplitude of each wave?
The amplitude is half of 0.372 =0.186 m
The speed is not affected by the amplitude, and hence remains the same.

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