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Sears and Zemansky's University Physics with Modern Physics | 13th Edition | ISBN: 9780321696861 | Authors: Hugh D. Young; Roger A. Freedman; A. Lewis Ford
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Answer: A fisherman notices that his boat is moving up and

Chapter 15, Problem 6E

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QUESTION:

Problem 6E

A fisherman notices that his boat is moving up 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 travelling? (b) What is the amplitude of each wave? (c) If the total vertical distance travelled by the boat were 0.30 m but the other data remained the same, how would the answers to parts (a) and (b) be affected?

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QUESTION:

Problem 6E

A fisherman notices that his boat is moving up 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 travelling? (b) What is the amplitude of each wave? (c) If the total vertical distance travelled by the boat were 0.30 m but the other data remained the same, how would the answers to parts (a) and (b) be affected?

ANSWER:

Solution 6E

Introduction

The given time is the time taken by the boat to reach from highest point of the wave (crest) and the lowest point (tough). We have to calculate the time period from this data. Then we can get the wave length from the separation between the wave. So using the time period and wavelength we can calculate the speed of the wave.

The amplitude is the crest and trough of the wave, which is given and hence we can easily calculate.

Then we have to get the same values for other given data.

Step 1

(a) The time taken by the boat to travel from highest to lowest point is equal to the half of the time period of the wave.

Hence the time period of the wave is

Now the separation between the wave crest is equal to the wavelength of the wave. Hence the wavelength is given by

Hence the speed of the wave is given by

Hence the wave is travelling at a speed of 1.2 m/s

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