Concept explainers
The fundamental frequency of the wire when the wire was half as long, twice as thick, and under one-fourth the tensionand the initial fundamental frequency is 256 Hz.
Answer to Problem 37SP
Solution:
Explanation of Solution
Given data:
The wire initially vibrates with the fundamental frequencyof
Formula used:
The formula for wavelength of wave is
Here,
The formula of volume of wire in form of diameter is
Here,
The relationship between mass and density is
Here,
The formula for transverse wave in string is
Here,
The relation between wavelength and string length for fundamental frequency is as follows:
Here,
Explanation:
Recall the expression of the volume of the wire:
Calculate the initial volume of the wire.
Substitute
Recall the relationship between mass and volume:
Calculate the initial mass of the wire.
Substitute
Recall the formula of speed of the wave in the wire:
Calculate the speed of the wave in the wire.
Substitute
Substitute
Substitute
Recall the formula of the fundamental wavelength:
Substitute
Recall the formula of the fundamentalfrequency of the wave:
Substitute
Similarly, write the equation for the fundamental frequency of the wave in the second condition.
Here,
Sincein the second condition, length of wire gets half of its initial length, twice of the initial thickness, or diameter, and one-fourth of the initial tension.
Therefore,
Substitute
Substitute
Substitute
Conclusion:
The fundamental frequency of the wire insecond condition is
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Chapter 22 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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