Concept explainers
A bar of dimensions
The elongation in a bar when clamped at one end and a stretching force of
Answer to Problem 38SP
Solution:
Explanation of Solution
Given data:
The dimensions of bar is
The mass of rod is
The frequency of fundamental tone of longitudinal vibration is
The force applied at the end of the bar is
Formula used:
Write the expression of density of rectangular bar.
Here,
Write the expression of speed of sound in a rectangular bar.
Here,
Write the expression of speed of longitudinal waves.
Here,
Write the expression of Young’s Modulus.
Here,
Explanation:
When the bar is clamped at its center and vibrates longitudinally, its ends are free. Therefore, the bar must have antinodes at its ends and a node at its center. The distance between node and antinode is
So, the expression for length of bar in terms of wavelength is,
Solve for
Substitute
The expression of speed of longitudinal waves is,
Substitute
The expression of density of rectangular bar is,
Substitute
The expression of speed of sound in a rectangular bar is,
Solve for
Substitute
Also, the expression of Young’s Modulus is,
Solve for
Substitute
Further, simplify the expression.
Conclusion:
The elongation in a bar when clamped at one end and a stretching force of
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Chapter 23 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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