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Consider a drum head of radius R.
Its motion is governed by the 𝒘𝒂𝒗𝒆 𝒆𝒒𝒖𝒂𝒕𝒊𝒐𝒏
Imposing the edges of the drum are fixed tells us
the "special" frequencies
The solution u_n(r,t) contains J₀(kr): the zeroth Bessel function
α_n is the nᵗʰ root of J₀(x)pic.twitter.com/8A7Twn4Zxi
Wave Speed
The wave speed 𝑣 is the speed at which the waves will propagate along the surface
𝑣² is proportional to the tension (per unit length) across the drumhead
𝑣² is inversely proportional to the mass (per unit area) of the drumpic.twitter.com/InGdrw8BqX
Something I found cool: Multiple boundary conditions in 2D can given the same spectra. Aka: You can't completely decipher the shape of a drum by listening to it! https://en.m.wikipedia.org/wiki/Hearing_the_shape_of_a_drum …
Thank you for putting this together - something about your thread has helped 'click things together' in my head! 
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