In Melde's experiment, 8 loops are formed with a tension of a 0. 75 N. If the tension is increased to four times then the number of loops produced will be

Melde's experiment is used to analyse the standing waves.

In this experiment, Tp² = Constant,

where T is tension in string and p is number of loops in the string.

$\Rightarrow {\mathrm{T}}_1{\mathrm{p}}_1^2={\mathrm{T}}_2{\mathrm{p}}_2^2$

$\Rightarrow {\mathrm{p}}_2^2=\frac{{\mathrm{T}}_1{\mathrm{p}}_1^2}{{\mathrm{T}}_2}$

As tension is increased to four times,

${\mathrm{p}}_2^2=\frac{{\mathrm{T}}_1{\mathrm{p}}_1^2}{4{\mathrm{T}}_1}=\frac{{\mathrm{p}}_1^2}{4}=\frac{8^2}{4}=16$

$\Rightarrow {\mathrm{p}}_2=4$