Concept explainers
(a)
The amplitude of the transverse wave on a string described by
(a)
Answer to Problem 25P
The amplitude of the transverse wave on the string is
Explanation of Solution
Write the standard expression of a transverse wave travelling along
Here,
Write the equation of wave given in question.
Conclusion:
Compare equation (II) with (I) to get
Therefore, the amplitude of the transverse wave on the string is
(b)
The wavelength of the transverse wave on a string described by
(b)
Answer to Problem 25P
The wavelength of the transverse wave on a string described by
Explanation of Solution
Write the standard expression of a transverse wave travelling along
Here,
Write the equation of wave given in question.
Expand above equation to compare with standard form given in equation (I).
Write the expression for wavelength of wave.
Conclusion:
Compare equation (III) with (I) to get
Substitute
Therefore, the wavelength of the transverse wave on a string is
(c)
The frequency of the transverse wave on a string described by
(c)
Answer to Problem 25P
The frequency of the transverse wave on a string described by
Explanation of Solution
Write the standard expression of a transverse wave travelling along
Here,
Write the equation of wave given in question.
Expand above equation to compare with standard form given in equation (I).
Write the expression for frequency of wave.
Conclusion:
Compare equation (III) with (I) to get
Substitute
Therefore, the frequency of the transverse wave on a string described by
(d)
The direction of the transverse wave on a string described by
(d)
Answer to Problem 25P
The transverse wave on a string described by
Explanation of Solution
Write the standard expression of a transverse wave travelling along
Here,
Write the equation of wave given in question.
Equation (I) represents a transverse traveling along
Conclusion:
The wave in equation (II) represents same type of wave that travels in
Therefore, the transverse wave on a string described by
(e)
The maximum transverse speed of a point on the string.
(e)
Answer to Problem 25P
The maximum transverse speed of a point on the. string described by
Explanation of Solution
Write the standard expression of a transverse wave travelling along
Here,
Write the equation of wave given in question.
Expand above equation to compare with standard form given in equation (I).
Write the expression for maximum transverse speed of a point on the string.
Conclusion:
Substitute
Therefore, the maximum transverse speed of a point on the. string described by
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