Concept explainers
A standing wave is described by the wave function
where x and y are in meters and t is in seconds. (a) Prepare graphs showing y as a function of x for five instants: t = 0, 5 ms, 10 ms, 15 ms, and 20 ms. (b) From the graph, identify the wavelength of the wave and explain how to do so. (c) From the graph, identify the frequency of the wave and explain how to do so. (d) From the equation, directly identify the wavelength of the wave and explain bow to do so. (e) From the equation, directly identify the frequency and explain how to do so.
(a)
To draw: The graphs showing
Answer to Problem 18.18P
The graph of
Figure (1)
The graph of
Figure (2)
The graph of
Figure (3)
The graph of
Figure (4)
The graph of
Figure (5)
Explanation of Solution
Introduction:
The values of
Explanation:
Given info: The sinusoidal waves function is,
For
Substitute
The graph of
Figure (1)
For
Substitute
The graph of
Figure (2)
For
Substitute
The graph of
Figure (3)
For
Substitute
The graph of
Figure (4)
For
Substitute
The graph of
Figure (5)
(b)
Answer to Problem 18.18P
Explanation of Solution
Given info: The sinusoidal waves function is
The distance between the two-crest point or two trough point is called the wavelength of the wave.
From the figure (1), the distance between the two crest point is
Conclusion:
Therefore, the wavelength of the wave is
(c)
Answer to Problem 18.18P
Explanation of Solution
Given info: The sinusoidal waves function is
Compare the equation (1) with
The frequency of the wave is,
Substitute
Conclusion:
Therefore, the frequency of the wave is
(d)
Answer to Problem 18.18P
Explanation of Solution
Given info: The sinusoidal waves function is
Compare the equation (1) with
The frequency of the wave is,
Substitute
Conclusion:
Therefore, the wavelength of the wave is
(e)
Answer to Problem 18.18P
Explanation of Solution
Given info: The sinusoidal waves function is
Compare the equation (1) with
The frequency of the wave is,
Substitute
Conclusion:
Therefore, the frequency of the wave is
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Chapter 18 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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