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Q.
In Melde's experiment, $8$ loops are formed with a tension of a $0.75N.$ If the tension is increased to four times then the number of loops produced will be -
NTA AbhyasNTA Abhyas 2020
Solution:
Melde's experiment is used to analyse the standing waves.
In this experiment, $Tp^{2}=\text{Constant}$ , where $T$ is tension in string and $p$ is number of loops in the string.
$\Rightarrow T_{1}p_{1}^{2}=T_{2}p_{2}^{2}\Rightarrow p_{2}^{2}=\frac{T_{1} p_{1}^{2}}{T_{2}}$
As tension is increased to four times, $p_{2}^{2}=\frac{T_{1} p_{1}^{2}}{4 T_{1}}=\frac{p_{1}^{2}}{4}=\frac{8^{2}}{4}=16$
$\Rightarrow p_{2}=4$