Physics - Wave on String Question with Solution | TestHub
A metallic wire of length , cross-sectional area , Young's modulus , and coefficient of linear thermal expansion is stretched between two rigid supports. It is initially under tension at temperature . If the temperature is raised to , and the wire's length is constrained to remain , what is the new fundamental frequency of transverse vibrations? Assume the linear mass density remains approximately constant.
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Solution:
When the temperature is raised by , the wire attempts to expand by . Since the supports are rigid, this expansion is prevented, leading to a decrease in tension. The change in tension is given by . The new tension is .
The fundamental frequency of transverse vibrations in a string fixed at both ends is . Substituting the new tension, the new fundamental frequency is .
