Question

If $L$ is the length of a stretched wire, $T$ is tension in the wire, $e$ is linear density of wire, the frequency of transverse vibrations of stretched wire is proportional to

• A. $L^1{T}^{1/2}{e}^{-1/2}$
• B. $L^1{T}^{-1/2}{e}^{-1/2}$
• C. $L^{-1}{T}^{1/2}{e}^{-1/2}$
• D. $L^{1/2}{T}^1{e}^{-1/2}$

Answer 1

The correct option is C $L^{-1}{T}^{1/2}{e}^{-1/2}$

frequency $v=\frac{V}{\lambda }$
but in case of stretched wire $\frac{\lambda }{\alpha }\propto L$
$\Rightarrow \lambda \alpha 2Z$
$V=\sqrt{\frac{T}{\mu }}$
$\therefore V\alpha \frac{1}{2L}\sqrt{\frac{T}{\mu }}$
$\therefore$ frequency is proportional to $L^{-1},T^{1/2}and{e}^{-1/2}$