Question

In Melde's experiment, when tension in the string is $10gwt$ then three loops are obtained. Determine the tension in the string required to obtain four loops, if all other conditions are constant.

Answer 1

Let us assume that the Fork is in perpendicular position for our convenience.

For this experiment, $N=\frac{p}{2l}\times \sqrt{\frac{T}{m}}$

Here N is the frequency, p is the number of loops, $l$ is length, T is tension and m is linear density of string.

It is mentioned that all conditions except the tension are constant.

Hence N will be equal for both.

$\therefore \frac{p_{{}_1}}{2l}\times \sqrt{\frac{T_1}{m}}=\frac{p_{{}_2}}{2l}\times \sqrt{\frac{T_2}{m}}$

$\frac{p_{{}_1}}{p_{{}_2}}=\sqrt{\frac{T_2}{T_1}}$

$\therefore T_2=\frac{p_{{}_1}^2\times T_1}{p_{{}_2}^2}=\frac{3^2\times 10}{4^2}=5.625$

$Answer:-$ $5.625$ $g$ $wt$