Concept explainers
(a)
The frequency of the wave.
(a)
Answer to Problem 16.13P
The frequency of the wave is
Explanation of Solution
Given info: The wavelength of wave is
The formula to calculate frequency of wave is,
Here,
Substitute
Conclusion:
Therefore, the frequency of the wave is
(b)
The angular frequency of the wave.
(b)
Answer to Problem 16.13P
The angular frequency of the wave is
Explanation of Solution
Given info: The wavelength of wave is
The formula to calculate angular frequency of the wave is,
Here,
Substitute
Conclusion:
Therefore, the angular frequency of the wave is
(c)
The angular wave number of the wave.
(c)
Answer to Problem 16.13P
The angular wave number of the wave is
Explanation of Solution
Given info: The wavelength of wave is
The formula to calculate angular wave number of the wave is,
Here,
Substitute
Conclusion:
Therefore, the angular wave number of the wave is
(d)
The wave function of the wave.
(d)
Answer to Problem 16.13P
The wave function of the wave is
Explanation of Solution
Given info: The wavelength of wave is
The formula of standard wave equation is,
Here,
Substitute
Conclusion:
Therefore, the function of the wave is
(e)
The equation of motion for the left end of string.
(e)
Answer to Problem 16.13P
The equation of motion for the left end of string is
Explanation of Solution
Given info: The wavelength of wave is
From equation (3),
For the left end of string the position coordinate
Substitute
Conclusion:
Therefore, the equation of motion for the left end of string is
(f)
The point on the string
(f)
Answer to Problem 16.13P
The equation of motion for the left end of string is
Explanation of Solution
Given info: The wavelength of wave is
From equation (3),
For the point
Substitute
Solve the above expression for
Conclusion:
Therefore, the equation of motion for the left end of string is
(g)
The maximum speed of element of the string.
(g)
Answer to Problem 16.13P
The maximum speed of element of string is
Explanation of Solution
Given info: The wavelength of wave is
From equation (3), the position of the wave is,
The change in position with respect to time gives the speed.
Differentiate above equation n with respect to time,
Here,
Substitute
Solve the above expression for
Substitute
As the cosine wave varies from the positive of
Conclusion:
Therefore, the maximum speed of element of string is
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Chapter 16 Solutions
Physics for Scientists and Engineers, Volume 1
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