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 tuning fork's fundamental is measured at 440Hz. Someone argues: "A tuning fork prong is just a small vibrating beam, and vibrating systems ring at whole-number multiples of their fundamental, like a guitar string. So the first overtone should be at 2×440=880Hz, and the clang I hear when I strike the fork hard must be that." Find the error in this reasoning, and give the correct frequency of the first overtone using the clamped-free (cantilever) eigenvalue ratio f1:f2:f3=1:6.27:17.5.