length of air column at frequency

Question

Water is poured into a long glass tube closed at one end. What length of air column must be left above the water level if the column is to reinforce and resonate at a frequency of 440 Hz?

Answer 1

A closed-ended tube will have resonance frequencies at odd-numbered quarter wavelengths. We can use the following equation to find the length of the air column:

f = (nv) / (4L)

f is the frequency, n is an odd-numbered integer to signify the different harmonics, v is the velocity of the wave, and L is the length of the air column.

We know that the speed of sound, v, is 343 m/s in air and that the fundamental frequency(n=1) is 440 Hz. Thus we can plug the values into the equation and solve for L:

440 = (1)(343) / (4)(L)

L = 343 / [(4)(440)] = 0.1948863636 m

L = 0.19 m