Physics-
General
Easy
Question
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
The correct answer is: ![f proportional to fraction numerator 1 over denominator L D end fraction](data:image/png;base64,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)
The fundamental frequency is
![f equals fraction numerator 1 over denominator 2 L end fraction equals square root of fraction numerator T over denominator mu end fraction end root](data:image/png;base64,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)
![f equals fraction numerator 1 over denominator 2 L end fraction equals square root of fraction numerator T over denominator rho pi fraction numerator d to the power of 2 end exponent over denominator 4 end fraction end fraction end root equals fraction numerator 1 over denominator L D end fraction square root of fraction numerator T over denominator pi rho end fraction end root](data:image/png;base64,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)
![therefore f proportional to fraction numerator 1 over denominator L D end fraction](data:image/png;base64,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)
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