Question

The length and diameter of a metal wire is doubled. The fundamental frequency of vibration will change from n to_______. (tension being kept constant and material of both the wires is same)

• A. $\frac{n}{2}$
• B. $\frac{n}{4}$
• C. $\frac{n}{12}$
• D. $\frac{n}{16}$

Answer 1

Answer: (B)

$\frac{n}{4}$

$f=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

Given,

$T_2=T_1,{\mu }_2=4{\mu }_1,L_2=2L_1$ $[\because A_2=4A_1]$

$\Rightarrow f_2=\frac{n}{4}$