Physics › Waves and Sound › Organ Pipe (Vibration of Air Column)
Two open organ pipes of fundamental frequencies $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ are joined in series.…
Two open organ pipes of fundamental frequencies $\mathrm{n}_{1}$ and $\mathrm{n}_{2}$ are joined in series. The fundamental frequency of the new pipe is
$\mathrm{n}_{1}-\mathrm{n}_{2}$ $\frac{n_{1} n_{2}}{\left(n_{1}+n_{2}\right)}$ $\frac{1}{n_{1} n_{2}}$ $\frac{n_{1}+n_{2}}{n_{1} n_{2}}$ Solution
$\mathfrak{n}=\frac{\mathrm{V}}{2 \ell_{1}} \quad \therefore \quad \ell_{1}=\frac{\mathrm{V}}{2 \mathrm{n}_{1}}$
$\mathfrak{n}_{2}=\frac{\mathrm{V}}{2 \ell_{2}} \quad \therefore \quad \ell_{2}=\frac{\mathrm{V}}{2 \mathrm{n}_{2}}$
$\mathfrak{n}=\frac{\mathrm{V}}{2 \ell} \quad \therefore \quad \ell=\frac{\mathrm{V}}{2 \mathrm{n}}$
$\ell=\ell_{1}+\ell_{2}$
$\frac{\mathrm{V}}{2 \mathrm{n}}=\frac{\mathrm{V}}{2 \mathrm{n}_{1}}+\frac{\mathrm{V}}{2 \mathrm{n}_{2}}$
$\therefore \frac{1}{\mathrm{n}}=\frac{1}{\mathrm{n}_{1}}+\frac{1}{\mathrm{n}_{2}}$
$\therefore \mathrm{n}=\frac{\mathrm{n}_{1} \mathrm{n}_{2}}{\mathrm{n}_{1}+\mathrm{n}_{2}}$
Asked in: MHT CET 2020 (14 Oct Shift 1)
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