The Helmholtz Resonator- What determines the characteristic frequency when you blow over the top of a bottle? A simple theory, without even appealing to the idea of normal modes was worked out by Helmholtz. The idea is to treat the air in the neck of the bottle as a moving mass and the air in the bulk of the bottle as a spring. To wit:
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The Helmholtz Resonator is analyzed. The Frequency when you blow over the top of a bottle is found.