A large church bell has a fundamental note of frequency

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Simple, damped and driven oscillations · Simple, damped and driven oscillations

Mathematical Methods for Physics, Ch Second-order linear equations: damping, driving and resonance

Problem

f_0 = 220\,\mathrm{Hz}

. After being struck, no further force acts on it, and its sound amplitude is measured to fall to

1/e

of its initial value after

t_e = 8.5\,\mathrm{s}

of free ringing. (a) Find the damping rate

\gamma

of the bell's oscillation. (b) Find the quality factor

Q

of the bell. (c) Find the half-power bandwidth

\Delta f

of the bell's resonance, in

\mathrm{Hz}

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