Question 25

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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