Concept explainers
(a)
The mas per unit length of the string.
(a)
Answer to Problem 73CP
The mas per unit length of the string is
Explanation of Solution
Write the equation for the mass per unit length.
Here,
Conclusion:
Substitute
Thus, the mas per unit length of the string is
(b)
The tension in the string.
(b)
Answer to Problem 73CP
The tension in the string is
Explanation of Solution
Write the equation for the fundamental frequency.
Here,
Write the equation for the speed.
Here,
Rewrite the expression for the tension by using (II) and (III).
Conclusion:
Substitute
Thus, the tension in the string is
(c)
The tension in the string at
(c)
Answer to Problem 73CP
The tension in the string at
Explanation of Solution
Write the equation for actual length.
Here,
Write the equation for the area of cross-section.
Here,
Rewrite the expression for the length at
Write the expression for the unstretched length at
Here,
Write the expression for the tension at
Here,
Conclusion:
Substitute
Substitute
Thus, the tension in the string at
(d)
The fundamental frequency.
(d)
Answer to Problem 73CP
The fundamental frequency is
Explanation of Solution
The frequency is directly proportional to the square root of tension.
Write the equation for new fundamental frequency.
Here,
Conclusion:
Substitute
Thus, the fundamental frequency is
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Chapter 19 Solutions
Physics for Scientists and Engineers with Modern, Revised Hybrid (with Enhanced WebAssign Printed Access Card for Physics, Multi-Term Courses)
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