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For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1 : 3 : 5$$ respectively. If the frequency of fifth harmonic is $$405$$ Hz and the speed of sound in air is $$324$$ m s$$^{-1}$$, the length of the organ pipe is _____ m.
Correct Answer: 1
A frequency ratio of $$1 : 3 : 5$$ indicates an organ pipe open at one end (closed pipe).
$$f_n = \frac{n v}{4L}$$
$$f_5 = 405 \text{ Hz}$$
$$v = 324 \text{ m/s}$$
$$405 = \frac{5 v}{4L}$$
$$405 = \frac{5 \times 324}{4L}$$
$$L = 1 \text{ m}$$
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