Concept explainers
(a)
The angular frequency of the wave.
(a)
Answer to Problem 11P
The angular frequency of the wave is
Explanation of Solution
Write the expression for the angular frequency of the wave.
Here,
The wave function of the given wave.
Use the trigonometric relation
Comparing equation (I) and (III).
Write the expression for the speed of the wave.
Conclusion:
Substitute,
Therefore, the angular frequency of the wave is
(b)
The wave number of the wave.
(b)
Answer to Problem 11P
The wave number of the wave is
Explanation of Solution
Write the expression wave number.
Here,
Write the expression for wavelength.
Conclusion:
Substitute,
Substitute,
Therefore, the wave number of the wave is
(c)
The wave function of the wave.
(c)
Answer to Problem 11P
The wave function of the wave is
Explanation of Solution
Write the general expression for wave function of a wave moving in positive
Here,
Conclusion:
Substitute,
Therefore, the wave function of the wave is
(d)
Themaximum transverse speed of the wave.
(d)
Answer to Problem 11P
Themaximum transverse speed of the wave is
Explanation of Solution
The derivate of vertical displacement gives the transverse speed of the wave.
Conclusion:
Substitute,
The maximum value of cos is 1. Therefore the maximum transverse speed is.
Therefore, the maximum transverse speed of the wave is
(e)
The maximum transverse acceleration of an element of the string.
(e)
Answer to Problem 11P
The maximum transverse accelerationof an element of the string is
Explanation of Solution
The transverse accelerationwill be equal to the derivative of transverse speed with respect to time.
Write the expression for the transverse acceleration.
Conclusion:
Substitute,
The maximum value of sine is 1. Therefore the maximum transverse acceleration is.
Therefore, the maximum transverse acceleration of an element of the string is
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Chapter 16 Solutions
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