Concept explainers
(a)
The possible frequencies for tuning the guitar string.
(a)
Answer to Problem 79PQ
The possible frequencies for tuning the guitar string either
Explanation of Solution
Write the expression for beat frequency
Here,
Conclusion:
Substitute
Therefore, the possible frequencies for tuning the guitar string either
(b)
The frequency of the guitar string, if the musician loosens the guitar string.
(b)
Answer to Problem 79PQ
The frequency of the guitar string, if the musician loosens the guitar string is
Explanation of Solution
If loosening the string lowers the wave speed and frequency, if the original frequency was
Write the expression for beat frequency, if the musician loosens the guitar string
Here,
Conclusion:
Substitute
Instead the frequency must have started at
Therefore, frequency of the guitar string, if the musician loosens the guitar string is
(c)
The percentage of the tension in the guitar string change for the string to be tuned to
(c)
Answer to Problem 79PQ
The percentage of the tension in the guitar string change for the string to be tuned to
Explanation of Solution
Write the expression for fundamental frequency depends on the tension in the string.
Here,
The ratio of the two frequencies then depends on the square root of the ratio of tensions.
Here,
Rearrange the above equation for
Conclusion:
The fractional change should be made in the tension is,
Rearrange the above equation and then compare with equation (IV).
Substitute
Therefore, the current tension should be reduced by a factor of 2.01% in order to bring the string in tune with the reference tone.
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Chapter 18 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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