Concept explainers
(a)
The fundamental frequency of the string.
(a)
Explanation of Solution
Given:
Linear mass density of the string is
Tension in the string is
One of the resonance frequency is
Other higher resonance frequency is
Formula used:
Write expression for
Here,
Rearrange above expression for
Write expression for
Here,
Substitute
Calculation:
Substitute
Conclusion:
Thus, fundamental frequency of the string is
(b)
The harmonic which has given frequencies.
(b)
Explanation of Solution
Given:
Linear mass density of the string is
Tension in the string is
One of the resonance frequency is
Other higher resonance frequency is
Formula used:
Write expression for
Here,
Rearrange above expression for
Write expression for
Here,
Substitute
Calculation:
Substitute
Substitute
Conclusion:
Thus, fifth harmonic has the given frequencies.
(c)
The length of the string.
(c)
Explanation of Solution
Given:
Linear mass density of the string is
Tension in the string is
One of the resonance frequency is
Other higher resonance frequency is
Formula used:
Write expression for
Here,
Rearrange above expression for
Write expression for
Here,
Substitute
Write expression for length of the string.
Here,
Calculation:
Substitute
Substitute
Conclusion:
Thus, the length of the string is
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Chapter 16 Solutions
Physics for Scientists and Engineers
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