Arturo O. answered • 05/20/16

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f_n = frequency of nth harmonic (n = 1,3,5,7,... for open/closed pipe)

f_n = v / lambda_n

L = length = n (lambda_n / 4) for the nth harmonic

lambda_n = 4 L / n

f_n = v / (4 L / n) = nv / (4L)

Harmonics of open/closed pipe are odd numbers only, so consecutive harmonics are separated by 2.

f_n+2 / f_n = [(n+2) v / (4L)] / [nv / (4L)] = (n+2) / n = 490 Hz / 350 Hz = 1.4

(n+2) / n = 1.4

n = 5

Therefore, the 350 Hz frequency is the 5th harmonic and the 490 Hz frequency is the 7th harmonic.

f_5 = 5 f_1 so f_1 = f_5 / 5 = 350 Hz / 5 =70 Hz

Similarly, f_1 = f_7 / 7 = 490 Hz / 7 = 70 Hz

The fundamental frequency is f_1 = 70 Hz.