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So for a research project I need to predict what the resonant frequency of a air column in a vessel will be . The problem is that these vessels are not cylindrical or any common shape. So I need to be able to mathematically calculate the resonant frequency of that air column. Is there a simple general method to approach this problem ?

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There is no simple, accurate, and general method, but you can pick any two of those three criteria.

Assuming the vessel can be considered rigid:

If the "column" of air is enclosed in something that looks approximately like a pipe or a set of connected pipes, you can get a reasonable approximation by piecing together the solution for sections of pipes with different cross sectional areas.

If the "vessel" has a small opening compared with its internal volume, it will behave approximately like a Helmholtz resonator.

In general, you have to solve the equation of motion of the air with the boundary conditions created by the shape of the container. If the vessel is not completely closed, there is a practical complication because the (infinite) volume of air outside the vessel also vibrates at the resonant frequency. Of course the outside vibration decays as the distance from the vessel increases, but the interaction between the shape of the "hole" and the surrounding shape of the vessel can be important. This is a generalization of the "end correction factor" that needs to be applied in simple physics lab experiments on the resonance of simple open tubes.

The practical way to do this is to use acoustic modelling software, which usually uses the Boundary Element method to handle the infinite solution domain outside the vessel. There is plenty of commercial closed-source and open source software available, but this isn't a "shopping site" so we can't make recommendations beyond "use google to find them".

If the vessel is flexible (which is the case for many musical instruments, for example) that introduces another layer of complexity. You need to create a solid mechanics model of the vessel itself (for example using finite element software) and couple that to the equations of motion of the air. There are commercial software packages that solve this type of problem - google for "fluid-structure interaction".

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