Exercise 15.6 15 A fisherman notices that his boat is moving up and down periodi

Question

Exercise 15.6 15

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 2.80s for the boat to travel from its highest point to its lowest, a total distance of 0.680m . The fisherman sees that the wave crests are spaced 6.80m apart.

Part A

How fast are the waves traveling?

Part B

What is the amplitude of each wave?

Part C

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

Part D

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

Explanation / Answer

Given that

The fisherman sees that the wave crests are spaced (lamda) = 6.80m apart

The distance between the lowest to highest distance is =0.680m

Half time period of the wave is given by =2.80s

Now speed of the wave is given by

v =f*lamda =(1/T)*lamda =1/(2*2.80s)*6.80m=1.214m/s

The amplitude of each wave is given by

A =(1/2) peak to peak distance =0.5*0.680 =0.34m

For the part c the speed remains the same as part a

The vertical distance is = 0.500m then the amplitude of the wave isgiven by 0.250m (half the vertical distance )

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