A metal wire is clamped between two vertical walls. At 20 °C the unstrained length of the wire is ex

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A metal wire is clamped between two vertical walls. At 20 °C the unstrained length of the wire is exactly equal to the separation between walls. If the temperature of the wire is decreased the graph between fundamental frequency (f) and temperature (T) of the wire is

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Sol. Fundamental frequency$f = \frac{nv}{2L}$f∝ v$v \propto \sqrt{F}$ (F is Tension in wire)$F = YA\left( \frac{\Delta L}{L} \right)$ $\frac{\Delta L}{L}$ = α∆TF = (YA α)∆T=(YA α)(T – 20°)f∝v ∝ $\sqrt{F} \propto \sqrt{(T - 20)}$

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