Question

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

Answer 1

Hint: To answer this question we have to begin the answer by writing the formula of the frequency. From that formula we have to derive the expression for the tension. Then we have to put the values that are mentioned in the question into the expression. This will help us to obtain the required answer to this question.

Complete step by step answer:
Let us assume that the Fork is in a perpendicular position for our easy understanding.
Then for this experiment we can write that:
$N = \dfrac{p}{{2l}} \times \sqrt {\dfrac{T}{m}} $
In the above expression,
N represents the frequency
P represents the number if loops
l represents the length
T represents the tension
m represents the linear density of the string
As we know that it is mentioned that all the other conditions except that of tension are constant. Hence we can write that N will be the same for both.
So, $\dfrac{{{p_1}}}{{2l}} \times \sqrt {\dfrac{{{T_1}}}{m}} = \dfrac{{{p_2}}}{{2l}} \times \sqrt {\dfrac{{{T_2}}}{m}} $
Hence this will signify that:
$\dfrac{{{p_1}}}{{{p_2}}} = \sqrt {\dfrac{{{T_2}}}{{{T_1}}}} $
So the value of ${T_2}$becomes:
${T_2} = \dfrac{{p_1^2 \times {T_1}}}{{p_2^2}} = \dfrac{{{3^2} \times 10}}{{{4^2}}} = 5.625$

Hence we can say that the tension in the strong required to obtain four loops, if all other conditions are constant is 5.625 g wt.

Note: We should know that the main principle on which the Melde’s experiment was based on was that the mechanical waves always travelled in a direction which is opposite and results in the formation of immobile points. These points are also known as nodes.
The main use of the Melde’s experiment is to determine the behaviour of the standing waves. By standing waves we mean that the two waves will be moving in a direction which is opposite to each other but still will have the same amplitude and frequency.