<written on 2020.2.18>
When you blow the top of a bottle, it usually makes a wind instrument-like sound. The pitch seems to be higher when there's less water in the bottle. How is this sound made? The answer is: helmholtz resonance.
When wind is blown to the top of the bottle's neck, it can be thought that air in the part of the bottle's neck resonates up and down. Since this is the only movement of air in the bottle(right after blowing), the sound woud also have its reason to this resonance. By calculating the change of temperature, pressure, and volume of air in the bottle due to the resonating 'chunk' of air, the frequency of the resonation can be derived.
In conslusion, the higher the specific heat, pressure, section area of bottle's neck, or the lower the density, volume, or height of bottles neck, the frequency/pitch of the sound made when blow becomes higher.
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