# Tuning Fork and Air Column

## Main Question or Discussion Point

The apparatus looks like this (see attached):

I understand that in order to resonane with the tuning fork the air inside the column must be vibrating at the same frequency as the fork. In addition, I understand that varying the amount of water in the tube increases or decreases the length of the column of air, and that resonance can occur at different lengths. I also understand that this problem can be modeled as a tube closed at one end and that only the odd harmonics are possible.

I have the following questions regarding this problem:

1) It seems to me that changing the amount of water in the tube does not change the wavelength and frequency of the air inside of the tube. All the pictures I've seen show that an increase in the amount of air in the tube indeed allows for a longer wave overall, but the wavelength, lambda, does not change at greater lengths. It seems to me that if the frequency of the tuning fork is locked, the wavelength must also be. Instead, by lowering the water level there is more room for the propogation of the sound wave in the tube and so you are effectively increasing the harmonic number, n as opposed to increasing the value of lambda as would occur if a woodwind or string instrument was lengthened. In other words, while lengthening the column of air allows for more wavelengths to fit inside the column, the value of each wavelength, lambda, remains constant. Is this accurate? If not, please explain.

2) If the above logic is correct, it would seem to me that lengthening the air portion would only serve to decrease the resonant frequencies of each harmonic, but not the frequency of the wave itself (as that is determined by the tuning fork). In other words, it seems to me that an increase in the amount of air will mean that each (odd) harmonic can be achieved at a lower frequency. This is from the equation "frequency of the nth harmonic = nv/4L" (v is constant). If lengthening the tube indeed serves to manually increase the harmonic numer (as reasoned above) while decreasing the resonant frequency of each harmonic, it would make sense to me that the tuning fork and the air column could be vibrating at the same frequency at progressively increasing lengths of the air column (by f = nv/4L). Is this logic accurate?

Thank you!

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I think the wavelength of the sound wave and therefore λ is actually constrained by the water column. The harmonic number just represents different possible modes of vibration and not something that changes with λ.