Concept explainers
(a)
To show: The left hand side of the given equation is
(a)
Answer to Problem 18.88CP
Explanation of Solution
Given info: The frequency of wave is
Write the expression of the
Multiply
Integrate the above equation over on period of time
The term
The left side of the equation is,
Conclusion:
Therefore, the left hand side of the given equation is
(b)
To show: The terms of the right hand side of the given equation involving
(b)
Answer to Problem 18.88CP
Explanation of Solution
Given info: The frequency of wave is
The part of the right hand of the equation (1) involving
Conclusion:
Therefore, the terms of the right hand side of the given equation involving
(c)
To show: The terms of the right hand side of the given equation involving
(c)
Answer to Problem 18.88CP
Explanation of Solution
Given info: The frequency of wave is
The part of the right hand of the equation (1) involving
The integration of the
Conclusion:
Therefore, the terms of the right hand side of the given equation involving
(d)
To show: The entire right hand side of the equation reduces to
(d)
Answer to Problem 18.88CP
Explanation of Solution
Given info: The frequency of wave is
The right hand side of the equation (1) is,
The integer
Substitute
Conclusion:
Therefore, the entire right hand side of the equation reduces to
(e)
To show: The Fourier series expansion for a square wave is
(e)
Answer to Problem 18.88CP
Explanation of Solution
Given info: The frequency of wave is
The general equation of
From the part (a), The value of
From the part (d), the value of
Therefore,
Substitute
Substitute
Substitute
Conclusion:
Therefore, the Fourier series expansion for a square wave is
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Chapter 18 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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