Lord Rayleigh versus Chladni and KFC Sanders: Who is correct about tuning forks?

The tuning fork is one of my favorite pieces of acoustical apparatus (as evidenced by three published papers in the American Journal of Physics and an article in Acoustics Today). A favorite problem (formerly used on final exams, and currently used as a hands-on activity) for the first-year graduate structural vibrations course I teach, requires students to read excerpts from four textbooks which make a statement about the boundary conditions for the tines of a tuning fork. Lord Rayleigh and Barton describe a tuning fork as two fixed-free bars joined at the base, while Chladni and Kinsler, Frey, Coppens, and Sanders describe a tuning fork as free-free bar bent into a U- shape. Who is correct? Students are required to measure the frequency spectrum of a tuning fork and match the resulting frequency ratios to what they would obtain by solving the boundary condition problem by treating the fork tines as a free-free or fixed-free bar undergoing flexural vibrations. This talk will work through the problem and will illustrate some of the pitfalls that often trip up students. And yes, the question of who is correct will be answered!