Concept explainers
(a)
The speed of the transverse wave on the string.
(a)
Answer to Problem 82P
The speed of the transverse wave on the string is
Explanation of Solution
Write the expression for the speed of transverse wave
Here,
Write the expression for linear density
From the expression of density of cylinder it is possible to obtain an expression for mass.
The density of cylinder
Here,
Hence from equation (III) the equation for mass of cylinder
Substitute equation (IV) in (III)
Thus, the expression of speed of transverse wave is
Conclusion:
Substitute
Therefore, the speed of the transverse wave on the string is
(b)
The fundamental frequency of transverse wave.
(b)
Answer to Problem 82P
The fundamental frequency of transverse wave is
Explanation of Solution
Write the expression for frequency of transverse wave
Here,
In a simplest standing wave vibration, distance between the nodes gives the length of the wire, and wavelength is the double of distance between nodes.
Here
Conclusion:
Substitute
Therefore, the fundamental frequency of transverse wave is
(c)
The speed of longitudinal wave.
(c)
Answer to Problem 82P
The speed of longitudinal wave is
Explanation of Solution
Write the expression for speed of longitudinal wave
Here,
Conclusion:
Substitute
Therefore, speed of longitudinal wave is
(d)
The fundamental frequency of transverse wave.
(d)
Answer to Problem 82P
The
Explanation of Solution
Write the expression for frequency of longitudinal wave
Here,
In a simplest standing wave vibration, distance between the nodes gives the length of the wire, and wavelength is the double of distance between nodes.
Here
Conclusion:
Substitute
Therefore, the fundamental frequency of longitudinal wave is
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