A hammer strikes a long steel rail once

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

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

Problem

A hammer strikes a long steel rail once, exciting bending (flexural) vibrations across a broad range of frequencies simultaneously at the point of the blow. A microphone stands some distance further along the rail. Bending waves on the rail obey the dispersion relation

\omega = \sqrt{EI/\rho A}\,k^2

derived for flexural waves. Rank the arrival times at the microphone of the wave components at

100\,\mathrm{Hz}

1000\,\mathrm{Hz}

and

4000\,\mathrm{Hz}

, and describe the sound the microphone records.

Browse the problem library