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Q.
A tuning fork of frequency $f$ produces $4beats$ for both $95cm$ and $100cm$ long sonometer wire. Value of $f$ is
NTA AbhyasNTA Abhyas 2022
Solution:
According the the data given in the problem
$l_{1}=95cml_{2}=100cm$
We know that
$n \propto \frac{1}{l}\therefore \frac{n_{1}}{n_{2}}=\frac{l_{2}}{l_{1}}$
It is given that beat frequency is $4Hz$ , so we can write
$\frac{n + 4}{n - 4}=\frac{100}{95}=\frac{20}{19}$
$\Rightarrow 19n+76=20n-80$
Solving it further
$n=156Hz$