A second circular drumhead is cut from a different membrane

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Partial differential equations and boundary-value problems · Special functions and orthogonal polynomials

Conditions of Validity, Ch Separation of variables as a chain of Sturm-Liouville problems

Problem

A second circular drumhead is cut from a different membrane, radius

a=0.12\,\mathrm m

and wave speed

c=140\,\mathrm{m\,s^{-1}}

, clamped at its rim and plucked into the same shallow-cone shape as the worked example,

f(r)=h(1-r/a)

, but raised only

h=8.0\,\mathrm{mm}

at the centre. ((a)) Find the mode frequencies

f_{0,1}

f_{1,1}

and

f_{0,2}

. ((b)) Find the first three coefficients

c_1

c_2

c_3

of the cone in the mode basis, and say whether they depend on the new radius

a

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