Wave motionHardBloom L3
Question
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
Options
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Solution
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∆T
F = (YA α)∆T
=(YA α)(T – 20°)
f∝v ∝ $\sqrt{F} \propto \sqrt{(T - 20)}$
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