The open G string of a guitar has fundamental frequency and quality factor

PHYSICS · Multi-part · 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

The open G string of a guitar has fundamental frequency

f_0 = 196\,\mathrm{Hz}

and quality factor

Q = 850

, found from the sharpness of its resonance. ((a)) Find the half-power bandwidth

\Delta f

of the resonance, in

\mathrm{Hz}

. ((b)) Find the damping rate

\gamma

of the plucked string's vibration. ((c)) Find the time after plucking for the string's vibration amplitude to fall to

1/e

of its initial value.

Browse the problem library