A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths…
A closed organ pipe and an open organ pipe have their first overtones identical in
frequency. Their lengths are in the ratio
$3: 4$
$2: 3$
$4: 5$
$1: 2$
Solution
First overtone of a closed pipe is given by
$\mathrm{f}=\frac{3 \mathrm{~V}}{4 \ell}$
First overtone of an open pipe is given by
$\mathrm{f}^{\prime}=\frac{\mathrm{V}}{\ell^{\prime}}$
Since $\mathrm{f}=\mathrm{f}^{\prime}, \quad \frac{3 \mathrm{~V}}{4 \ell}=\frac{\mathrm{V}}{\ell^{\prime}}$
$\therefore \frac{\ell}{\ell^{\prime}}=\frac{3}{4}$