How Low Can a Pop Bottle Go in Pitch?

[Numzie]

Is there a theoretical limit to the lowest note achievable in a closed tube(Pop bottle)?

Heres the question in context:
I've got what I believe to be the correct:
http://img141.imageshack.us/img141/9301/1azw1.jpg
^^ May want to check that, if you don't mind ^^

 

[Numzie]

I've searched all over for something but can't find anything. From what I can reason there would be a limit for two reasons:
1) Because the human ear can only hear a limited about of frequencies.(I assume this is correct but doesn't really relate to the given situation)
2) Frequency and wavelength are inversely proportional so eventually at a low enough frequency the wavelength will be so great that 1/4 of its wavelength is greater than the length of the tube.