Concept explainers
(a)
The period and wavelength of the wave.
(a)
Answer to Problem 19PQ
The period of the wave is
Explanation of Solution
Given the wave equation of the longitudinal harmonic wave.
Write the general equation of a longitudinal harmonic wave traveling in positive
Here,
Compare equation (I) and (II) to find the values of
Write the expression for the period of the wave.
Here,
Write the expression for the wavelength of the wave.
Conclusion:
Substitute
Substitute
Therefore, the period of the wave is
(b)
The displacement of the particle at
(b)
Answer to Problem 19PQ
The displacement of the particle at the given instants of time are given in Table 1.
Explanation of Solution
Given that the equilibrium position of the particle is
Equation (II) is the general expression a longitudinal harmonic wave traveling in positive
Equation (III) gives the expression for the period of the wave.
Equation (IV) gives the expression for the wavelength of the wave.
Use equation (III) and (IV) in (II).
In order to find the displacement
Conclusion:
Substitute
Table 1
Period | Time | |
Therefore, the displacement of the particle at the given instants of time are given in Table 1.
(c)
The position of the particle at
(c)
Answer to Problem 19PQ
The position of the particle at the given instants of time are given in Table 2.
Explanation of Solution
Given that the equilibrium position of the particle is
Table 1 gives the displacement of the particle at different times. At
Conclusion:
The position of the particle corresponding to the other times given can be computed by adding the displacement corresponding to the respective time with the initial position
Table 2
Period | Time | Position ( | |
Therefore, the position of the particle at the given instants of time are given in Table 2.
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Chapter 17 Solutions
Student Solutions Manual For Katz's Physics For Scientists And Engineers: Foundations And Connections, Volume 1
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