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A metallic wire with tension T and at temperature 30° C vibrates with its fundamental frequency of 1 kHz. The same wire under the same tension but at 10° C temperature vibrates with a fundamental frequency of 1.001 kHz. The coefficient of linear expansion of the wire is

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$1.5 \times 10^{- 4} /^{0} C$

$0.5 \times 10^{- 4} /^{0} C$

$2 \times 10^{- 4} /^{0} C$

$1 \times 10^{- 4} /^{0} C$

answer is C.

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Detailed Solution

$\begin{array}{l} f = \frac{1}{2 l} \sqrt{\frac{T}{\frac{m a s s}{l}}} = \frac{1}{2} \sqrt{\frac{T}{m a s s l}} \\ f α \frac{1}{\sqrt{l}} \\ \frac{Δ f}{f} = - \frac{1}{2} \frac{Δ l}{l} = - \frac{1}{2} α θ \end{array}$

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