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A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 445.0 Hz. The next higher harmonic has a frequency of 525.9 Hz. The speed of sound in air is 343 m/s.
(a) What is the integer n that describes the harmonic whose frequency is 445.0 Hz?

(b) What is the length of the tube?
m


(a) The ratio of frequencies is the ratio of harmonic dumbers. In your case it is 525.9/445.0 = 1.1818, which is very nearly 13/11. Therefore 13 and 11 are the two "n" numbers involved. Tubes open at one end only have only odd numbered hamonics. The number "n" corresponds to the number of quarter-waves in the pipe.

(b) If a note corresponds to a n'th harmonic, the length of the pipe is n quarter waves. Get the wavelength from the sound speed and frequency.
wavelength = (sound speed)/frequency

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