Height of a Wave As a wave passes by an offshore piling, the height of the water is modeled by the function
where h(t) is the height in feet above mean sea level at time t seconds.
- (a) Find the period of the wave.
- (b) Find the wave height, that is, the vertical distance between the trough and the crest of the wave.
(a)
To find: The period of the wave for given function.
Answer to Problem 77E
The period of the function
Explanation of Solution
Formulas used:
The cosine curve
Given:
The height of the water is modeled by the function
Calculation:
The height of the water is modeled by the function
Here, the
The period of the wave is computed as follows,
Therefore, the period of the function
(b)
To find: The wave height, that is, the vertical distance between the trough and the crest of the wave.
Answer to Problem 77E
The wave of the height is 6 feet.
Explanation of Solution
Calculation:
The wave height is computed as follows,
The amplitude of the function
That is, the amplitude of the function is 3.
The height of wave is the apparent depth of crest and trough.
Then, the height is calculated as follows,
Therefore, the wave of the height is 6 feet.
The graph of the function as shown below in Figure 1.
From Figure 1, the graph of the function is periodic function and it has maximum value is 3 and minimum value is −3.
Chapter 5 Solutions
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