Question

A sonometer wire vibrating in fundamental mode is in unision with a tuning fork. Keeping the same tension, the length of the wire between the bridges is doubled the tuning fork can be in resonance with the wire. Provided the wire now vibrates in

• A. $4$ segments
• B. $6$ segments
• C. $3$ segments
• D. $2$ segments

Answer 1

The correct option is D $2$ segments

Let the initial length of wire is $l.$

$=\frac{v}{2l}=+$ ---------------$\left(1\right)$

Now$,$ new length $=2l.$

let it vibrates in n segments

$=n.\frac{v}{2\left(2l\right)}=+$

$=n.\frac{v}{4l}=\frac{v}{2l}$

$=n=2$

Hence$,$ option $\left(D\right)$ is correct$.$