Discussion
The ratio between the wavelengths of the air column vibrating in the first two modes in an open organ pipe is
Answer: A
The ratio is 2 : 1.
An open pipe has antinodes at both ends. Its modes fit whole half-wavelengths into the length L: \(L = \frac{n\lambda_{n}}{2}\), so \(\lambda_{n} = \frac{2L}{n}\).
\[ \lambda_{1} : \lambda_{2} = 2L : L = 2 : 1 \]
The frequencies are in the reverse ratio, 1 : 2, the trap answer. 1 : 3 describes the frequencies of the first two modes of a closed pipe, which has only odd harmonics.
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