Concept explainers
(a)
The frequency of the wave at
(a)
Answer to Problem 13P
The frequency of the wave at
Explanation of Solution
Writ the expression for frequency.
Here,
Conclusion:
Substitute,
Therefore, the frequency of the wave at
(b)
The angular frequency of the wave.
(b)
Answer to Problem 13P
The angular frequency of the wave is
Explanation of Solution
Write the expression for the angular frequency of the wave.
Conclusion:
Substitute,
Therefore, the angular frequency of the wave is
(c)
The wavenumber of the wave.
(c)
Answer to Problem 13P
The wavenumber of the wave is
Explanation of Solution
Write the expression for wavenumber in terms of wave length.
Here,
Conclusion:
Substitute,
Therefore, the wavenumber of the wave is
(d)
The wave function of the wave.
(d)
Answer to Problem 13P
The wave function of the wave is
Explanation of Solution
Write the general expression for wave function of a wave moving in positive
Here,
The amplitude of the given wave is
Conclusion:
Substitute,
Therefore, the wave function of the wave is
(e)
The equation of motion at the left end of the string.
(e)
Answer to Problem 13P
The equation of motion at the left end of the string is
Explanation of Solution
The left end of the string is considered as the origin. Thus at left end,
The wave function of the wave is.
Conclusion:
Substitute,
Therefore, the equation of motion at the left end of the string is
(f)
The equation of motion at
(f)
Answer to Problem 13P
The equation of motion at
Explanation of Solution
Write the expression for wave function of the wave.
Conclusion:
Substitute,
Therefore, the equation of motion at
(g)
The maximum speed of any element on the string.
(g)
Answer to Problem 13P
The maximum speed of any element on the string is
Explanation of Solution
The maximum speed will be obtained by taking the derivative of the position of the wave.
Consider the wave function of the wave.
The expression for maximum speed is.
Conclusion:
Substitute,
The value of cosine is in between
Therefore, the maximum speed of any element on the string is
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Chapter 16 Solutions
Physics For Scientists And Engineers With Modern Physics, 9th Edition, The Ohio State University
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