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Concept explainers
(a)
The two resonant frequencies.
(a)
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Explanation of Solution
Given:
The distance between nodes for first case is
The distance between nodes for second case is
Formula used:
Write expression for the wavelength of the wave.
Here, d is the distance between two nodes.
Write expression for frequency.
Here,
Substitute
Calculation:
Substitute
Substitute
Conclusion:
Thus, the two frequencies are
(b)
The fundamental frequency of the tube.
(b)
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Explanation of Solution
Given:
The distance between nodes for first case is
The distance between nodes for second case is
Formula used:
Write expression for the wavelength of the wave.
Here, d is the distance between two nodes.
Write expression for frequency.
Here,
Substitute
Write expression for frequency of
Rearrange above expression for
Write expression for next resonance.
Substitute
Calculation:
Substitute
Substitute
Substitute
Conclusion:
Thus, the fundamental frequency is
(c)
The value of
(c)
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Explanation of Solution
Given:
The distance between nodes for first case is
The distance between nodes for second case is
Formula used:
Write expression for the wavelength of the wave.
Here, d is the distance between two nodes.
Write expression for frequency.
Here,
Substitute
Write expression for frequency of
Rearrange above expression for
Write expression for next resonance.
Rearrange above expression for
Substitute
Calculation:
Substitute
Substitute
Substitute
Substitute
Substitute
Conclusion:
Thus, the value of
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Chapter 16 Solutions
Physics for Scientists and Engineers
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