A circular drumhead of radius

PHYSICS · Subjective · Fermi University Physics · Mathematical Methods for Physics · Partial differential equations and boundary-value problems · Partial differential equations and boundary-value problems

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

Problem

a = 0.20\,\mathrm{m}

, wave speed

c = 150\,\mathrm{m\,s^{-1}}

, has a disc of radius

0.06\,\mathrm{m}

removed from a point on its rim (a "bite"), and the remaining membrane is clamped along its entire boundary. The largest disc that fits inside the bitten membrane, clear of the bite, has radius

0.17\,\mathrm{m}

, centred

0.03\,\mathrm{m}

from the original centre, away from the bite. Estimate an upper and a lower bound on the fundamental frequency

f_1

of the bitten drum.

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