Two tuning forks $A$ and $B$ produce $8\ beats/s$ when sounded together. A gas column $37.5\ cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5\ cm$ of the same gas in a similar pipe is required for a similar resonance with fork $B$. The frequencies of these two tuning forks, are
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For tuning fork $'A'\frac{{{\lambda _1}}}{4} = 37.5$
so $n_{1}=\frac{v}{\lambda_{1}}=\frac{v}{4 \times 37.5}$
For tuning fork $'B'$ $\frac{\lambda_{2}}{4}=38.5$
$\therefore n_{2}=\frac{v}{\lambda_{2}}=\frac{v}{4 \times 38.5}$
$\therefore n_{1}-n_{2}=8 \Rightarrow \frac{v}{4 \times 37.5}-\frac{v}{4 \times 38.5}=8$
$\therefore v=(8 \times 4 \times 37.5 \times 38.5)$
$n_{1}=\frac{8 \times 4 \times 37.5 \times 38.5}{4 \times 37.5}=308 \mathrm{\,Hz}$
and $n_{2}=308-8=300 \mathrm{\,Hz}$
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