Concept explainers
(a)
The amplitude of the wave.
(a)
Answer to Problem 20P
The amplitude of the wave is
Explanation of Solution
The standard expression for the wave function of a wave is.
Here,
At
Write the expression of wave function at
The speed of the wave is obtained by taking the derivative of equation (I). the speed of the wave at
Substitute equation (I) in (II).
Write the expression for angular frequency in terms of time period.
Here,
The trigonometric identity
Multiply and divide the first term by
Substitute,
Conclusion:
Substitute,
Substitute,
Therefore, the amplitude of the wave is
(b)
The initial phase angle.
(b)
Answer to Problem 20P
The initial phase angle is
Explanation of Solution
Derive an expression for
Rewrite equation (VI) to obtain an expression for
Conclusion:
Substitute,
The value of
Therefore, the initial phase angle is
(c)
The maximum transverse speed of the elements in the string.
(c)
Answer to Problem 20P
The maximum transverse speed of the elements in the string is
Explanation of Solution
The transverse speed is already determined in part (a).
The maximum value of cosine is 1.
Thus, the expression for maximum transverse speed is.
Conclusion:
Substitute,
Therefore, the maximum transverse speed of the elements in the string is
(d)
The wave function of the wave.
(d)
Answer to Problem 20P
The wave function of the wave is
Explanation of Solution
Consider equation (I) which is the standard expression for wave function.
Write the expression for wavelength.
Here,
Write the expression for wave number.
Conclusion:
Substitute,
Substitute,
Substitute,
Therefore, the wave function of the wave is
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Chapter 16 Solutions
Physics for Scientists and Engineers with Modern Physics Technology Update
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