Question

In a sonometer experiment, the bridge are separated by a fixed distance. The wire which is slightly elastic, emits a tone of tension is increased to 4T, the tone emitted by the wire will be of frequency

• A. n
• B. 2n
• C. Slightly greater than 2n
• D. Slightly less than 2n

Answer 1

The correct option is D Slightly less than 2n

$n=\frac{1}{2L}\sqrt{\frac{T}{\pi r^2\rho }}$

If the tension is increased the wire gets elongated.

$\therefore n^{\prime }=\frac{1}{2l^{\prime }}\sqrt{\frac{4T}{\pi r^{\prime 2}\rho }}$

$\frac{n^{\prime }}{n}=2(\frac{l}{l^{\prime }}\times \frac{r}{r^{\prime }})$

Now mass remains the same,

$\therefore \pi r^{2}ld=\pi r^{\prime 2}{l}^{\prime }d$

$\frac{r}{r^{\prime }}=\sqrt{\frac{l^{\prime }}{l}}$

Therefore,

$\frac{n^{\prime }}{n}=2\sqrt{\frac{l}{l^{\prime }}}$

Here $l^{\prime }$ is slightly greater than $l$

So, $n^{\prime }$ is slightly less than $2n$