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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?

(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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