A sonometer wire of length $25 \mathrm{~cm}$ vibrates in unison with a tuning fork. When its length in…
A sonometer wire of length $25 \mathrm{~cm}$ vibrates in unison with a tuning fork. When its length in decreased by $1 \mathrm{~cm}, 6$ beats are heard per second. What is the frequency of the tuning fork?
$200 \mathrm{~Hz}$
$72 \mathrm{~Hz}$
$100 \mathrm{~Hz}$
$144 \mathrm{~Hz}$
Solution
When length decrease, the frequency of wire will increase. If $n$ is the frequency of the tuning fork, then we have
$\begin{aligned}
& \mathrm{n} \times 25=(\mathrm{n}+6) \times 24 \\
& \therefore \mathrm{n}=144 \mathrm{~Hz}
\end{aligned}$