A closed organ pipe and an open organ pipe emit notes of the same pitch. The ratio of the length of the air column in the closed pipe to that of the open pipe is ____________
Explanation
If the notes are of the same pitch, it means they are of the same frequency. The fundamental note of a closed pipe is given as:
\(f_0=\frac{V}{4 L}, L=\frac{V}{4 f_0}\)
The fundamental note of an open pipe is given as:
\(\mathrm{f}_0=\frac{\mathrm{V}}{2 \mathrm{~L}}, \mathrm{~L}=\frac{\mathrm{V}}{2 \mathrm{f}_0 .}\).
Since the frequency is the same, we can proceed that:
Lclosed \(^{\text {Lopen }}=\frac{V}{4 r_0} \div \frac{V}{2 r_0}\)
\(=\frac{\mathrm{V}}{4 f_0} \times \frac{2 f_0}{V}=\frac{2}{4}=1: 2\)
