Concept explainers
(a)
The transverse speed of the wave.
(a)
Answer to Problem 15P
The transverse speed of the wave is
Explanation of Solution
Write the general expression for wave function of a wave moving in positive
Here,
The wave function of the given wave.
The transverse speed will be obtained by taking the derivative of the position of the wave.
The expression for maximum speed is.
Conclusion:
Substitute,
Substitute,
Therefore, the transverse speed of any element on the string is
(b)
The transverse acceleration at
(b)
Answer to Problem 15P
The transverse acceleration at
Explanation of Solution
Transverse acceleration will be obtained by taking the derivative of transverse velocity with respect to time.
Write the expression for transverse acceleration.
Conclusion:
Substitute,
Substitute,
Therefore, the transverse acceleration at
(c)
The wavelength of the wave.
(c)
Answer to Problem 15P
The wavelength of the wave is
Explanation of Solution
Write the expression for wavelength of the wave in terms of wave number.
Here,
Comparing equation (I) and (II), the wave number is
Conclusion:
Substitute,
Therefore, the wavelength of the wave is
(d)
The period of the wave.
(d)
Answer to Problem 15P
The period of the wave is
Explanation of Solution
Write the expression for the period of the wave.
Here,
Comparing equation (I) and (II), the angular frequency is
Conclusion:
Substitute,
Therefore, the period of the wave is
(e)
The speed of an element of propagation of wave.
(e)
Answer to Problem 15P
The speed of an element of propagation of wave is
Explanation of Solution
Write the expression for speed.
Conclusion:
Substitute,
Therefore, the speed of an element of propagation of wave 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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