Thanks to Erik Petersen for consulting on this project.
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Helmholtz resonance, or air cavity resonance, refers to the resonance of air in a container with a small opening, like a plastic bottle or the devices shown in Figure 1. The resonant frequency of the air depends on the volume of the air in the container and the geometry of the opening (its length and cross-sectional area). The Helmholtz frequency is not the same as the natural frequency of an air column in a cylinder, where the opening is the same size and shape as the rest of the cylinder.
You can find the equations for both scenarios in the Bibliography section. Try using these equations to predict the frequency of sounds generated by a musical instrument, or you can make your own simple instruments using plastic bottles. You can measure the actual frequency using a pitch detector or audio spectrogram app on your phone. Which equation is more accurate for various geometries? How close are the results? For example, try comparing wide- and narrow-mouthed plastic bottles, plastic bottles with different levels of water in them, or different notes played on the same musical instrument. How well do your measured results match your predictions using the equations?
You can also analyze the model for Helmholtz resonance in more detail. For example, how do you define where the cavity ends and the neck begins? How much of a difference does this choice make? Try calculating the resonant frequency for high-end and low-end estimates of the neck length. Does the measured frequency fall within these two values?
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