A metallic wire with tension T and at temperature 30^ C vibrates with its fundamental frequency of 1 kHz . The same wire with 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

Step-by-step solution

Frequency of wire n= 1 2 l T m m= mass per unit length In both the condition same wire is kept same tension. So, aligned n₁ n₂ = l₂ l₁ 1 1.001 & = l₂ l₁ l₂ & = l₁ 1.001 aligned Fall in temperature t=30-10=20^ C aligned l₂ & =l₁(1- t) l₁ 1.001 & =l₁(1- 20) 1- 20 & = 1 1.001 = 0.001 1.001 = 1 1001 20 & =0.5 10⁻⁴ / ^ C aligned