Concept explainers
(a)
To show: The left hand side of the given equation is
(a)
Answer to Problem 50CP
The left hand side of the given equation is
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 50CP
The terms of the right hand side of the given equation involving
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 50CP
The terms of the right hand side of the given equation involving
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 50CP
The entire right hand side of the equation reduces to
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 50CP
The Fourier series expansion for a square wave is
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 17 Solutions
Physics for Scientists and Engineers with Modern Physics