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

Question

Exercise 15.6

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.30 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 7.60 m apart.

Part A

How fast are the waves traveling?

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Part B

What is the amplitude of each wave?

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Part C

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

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Part D

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

Exercise 15.6

A fisherman notices that his boat is moving up and down periodically, owing to waves on the surface of the water. It takes 3.30 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 7.60 m apart.

Part A

How fast are the waves traveling?

v =   m/s  

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Part B

What is the amplitude of each wave?

A =   m  

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Part C

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

v =   m/s  

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Part D

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

Explanation / Answer

It takes 3.3 s for boat to travel from its highest point to its lowest
So period, T = 2*3.3 s = 6.6 s
f = 1/T = 1/6.6 = 0.152 Hz

wave crests are spaced 7.60 m apart means wavelength = 7.6 m

Total distance from highest point to the lowest = 0.63 m
So, amplitude = 0.63/2 = 0.315 m

A)
speed of wave = wavelength * frequancy
= 7.6 m * 0.152 Hz
= 1.152 m/s

B)
amplitude as calculated above = 0.315 m

C)
Here amplitude will not change
But amplitude doesn't effect the speed
so, speed will still be 1.152 m/s

D)
Amplitude = 0.5/2 = 0.25 m

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