I read that wine bottle produces sound when u blow sideways onto its rim because some frequencies of the white noise produced in your mouth gets amplified when they match the natural frequency of the bottle. But is the tight neck of the bottle necessary for this to happen? If I blow into a closed end tube with uniform width, can't I produce the same effect? Why do I need the small opening?
The classic form of such a resonator is that of a bottle of uniform cylindrical shape, topped off with a much smaller tube. In this case, the air inside the bottle behaves like a spring and the air trapped in the tube acts like a mass- and you get a resonance at a well-defined frequency, at which the mass of air in the tube is bouncing off the springiness of the air in the bottle. Such a resonating system is called a lumped system and its analysis is straightforward.
Things get more complicated when the bottle tapers down into a neck, because then you must account for the fact that the air in the tapered section has not just mass but also a significant amount of springiness which you cannot ignore when predicting the bottle's resonant frequency. In this case, the resonant frequency will change and the resonance will not be so sharp.
Things get more complicated still when considering a tube with no taper in it, because in this case you have to account for both the mass and springiness of every element of air volume inside the tube. Such a resonating system is called a distributed system and its analysis is far more complicated.