It is well known that if you blow horizontally on a bottle top it creates a sound. Pouring water to the bottle changes the pitch.
I have been doing experiments on the relation between the sound's main frequency (or rather the corresponding wavelength) and the vertical distance between the bottle top and the water level.
My (poor) theoretical thoughts were that by blowing on the top I create a standing wave exactly between the bottle top and the water surface, therefore the wavelength should be equal to the height of the air column.
Apparently, I was wrong, but not completely -- it's not $y=x$, but rather a linear relation $y=ax+b$. I have been conducting several experiments with different bottles, and the results are:
A 18cm high bottle gave me $a=5.5$ and $b=26.65$. A 21.7cm bottle gave me $a=7.94$ and $b=14.54$. A tall 32.5cm bottle resulted in $a=7.1$ and $b=34.21$. But my biggest surprise was to find a negative $b$, with a glass 19.3cm bottle (the rest were plastic), and $a=9.16$ and $b=-22.43$.
Is there a plausible explanation for this phenomenon?
(I didn't consider the actual shape of the bottle as I assumed a vertical standing wave will emerge. Most of the bottles are pretty constant in shape, except for the glass bottle which is closer to a cone. Looking at the signal itself one can clearly see a high energy peak at the pitch, and smaller peaks at the pitch's multiples. I noticed that the slopes are close to natural numbers or half thereof.)