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  4. Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in 2 s. The initial frequency of each wire is

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Q. Two stretched wires are in unison. If the tension in one of the wire is increased by 1%, 3 beats are produced in $2 \, s.$ The initial frequency of each wire is

NTA AbhyasNTA Abhyas 2022

Solution:

$n_{1}=k\sqrt{T}, \, n_{2}=k\sqrt{1.01 T}$
$\because \, n_{2}-n_{1}=\frac{3}{2}$
$k\left(\sqrt{1.01 T} - \sqrt{T}\right)=1.5$
$k\sqrt{T}\left[\left(1 + 0.01\right)^{\frac{1}{2}} - 1\right]=1.5$
$k\sqrt{T}\left[1 + \frac{1}{2} \times 0.01 - 1\right]=1.5$
$k\sqrt{T}=\frac{1.5 \times 2}{0.01}$
$=\frac{1.5 \times 2}{0.01}$
$=300 \, Hz$