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.

 

[ogb p]

I can confirm that the concept of closed cylinder resonance does have a theoretical limit to the lowest note achievable in a closed tube, such as a pop bottle. This limit is determined by the length of the tube and the speed of sound in the medium (in this case, the air inside the bottle).

The lowest note achievable in a closed tube is known as the fundamental frequency, and it is directly proportional to the length of the tube. This means that the longer the tube, the lower the fundamental frequency and thus the lower the note that can be produced. However, there is a limit to how long a tube can be before it becomes impractical or impossible to produce a sound.

In the case of a pop bottle, the length of the bottle is relatively short, so the fundamental frequency will also be relatively high. This is why it is difficult to produce very low notes using a pop bottle as a musical instrument.

Additionally, the speed of sound in air is also a limiting factor for the lowest note achievable in a closed tube. The speed of sound is affected by factors such as temperature, humidity, and pressure, but on average it is around 343 meters per second. This means that even if the length of the tube is increased, there will be a point where the frequency of the sound wave produced will be too low for the speed of sound in air, and the sound will not be able to propagate through the tube.

In summary, while there is a theoretical limit to the lowest note achievable in a closed tube, it is also limited by practical and physical factors such as the length of the tube and the speed of sound in the medium. This means that while a pop bottle can produce relatively low notes, there is a limit to how low it can go due to its size and the properties of air.