TITLE: Determining the Frequency of a Gong
QUESTION [1 upvotes]: I want to build a circular Gong for Sound Healing and I want a specific frequency but I don't know how to calculate it.
Does someone can help me?

REPLY [2 votes]: Assuming we can model the problem in a similar way to the vibrations that occur on a drum skin, the problem you need to solve is 2 dimensional wave equation give by
$\frac{\partial^2 u(r,t)}{\partial t^2}=\frac{1}{c^2}\bigg(\frac{\partial^2 u(r,t)}{\partial r^2}+\frac{1}{r}\frac{\partial u(r,t)}{\partial r}\bigg)$
with open boundary conditions at the edges the problem becomes non-standard since in most cases Dirichlet boundary conditions are applied at the boundary edge giving the usual drum-skin solutions. The boundary condition you need to apply is $\frac{\partial u}{\partial r}\big\rvert_{r=a}=0$. A good PDF with an example is http://web.math.ucsb.edu/~grigoryan/124A/lecs/lec18.pdf.
{"set_name": "stack_exchange", "score": 1, "question_id": 477610}