A free-free brass rod is struck sharply on one end

PHYSICS · Subjective · Fermi University Physics · Oscillations, Waves & Acoustics · Fluids & Continuum Physics · Vibrating bodies, musical and architectural acoustics

Bending, Ringing, Breaking and Flowing, Ch Vibrations of rods, beams and plates

Problem

A free-free brass rod is struck sharply on one end. Piezoelectric pickups at the free ends show that its fundamental longitudinal ringing frequency is

f_L = 2000\,\mathrm{Hz}

and its fundamental torsional ringing frequency is

f_T = 1220\,\mathrm{Hz}

. Both fundamentals have the same mode shape (a single node at the centre, wavelength

2L

), so each frequency is

f = c/2L

with the appropriate wave speed,

c_{\rm bar} = \sqrt{E/\rho}

for stretching and

c_T = \sqrt{G/\rho}

for twisting. Find the Poisson's ratio of the brass.

Browse the problem library