A violin shell model: vibrational modes and acoustics.

A generic physical model for the vibro-acoustic modes of the violin is described treating the body shell as a shallow, thin-walled, guitar-shaped, box structure with doubly arched top and back plates. comsol finite element, shell structure, software is used to identify and understand the vibrational modes of a simply modeled violin. This identifies the relationship between the freely supported plate modes when coupled together by the ribs and the modes of the assembled body shell. Such coupling results in a relatively small number of eigenmodes or component shell modes, of which a single volume-changing breathing mode is shown to be responsible for almost all the sound radiated in the monopole signature mode regime below ∼1 kHz for the violin, whether directly or by excitation of the Helmholtz f-hole resonance. The computations describe the influence on such modes of material properties, arching, plate thickness, elastic anisotropy, f-holes cut into the top plate, the bass-bar, coupling to internal air modes, the rigid neck-fingerboard assembly, and, most importantly, the soundpost. Because the shell modes are largely determined by the symmetry of the guitar-shaped body, the model is applicable to all instruments of the violin family.

Violin bow vibrations.

The modal frequencies and bending mode shapes of a freely supported tapered violin bow are investigated by finite element analysis and direct measurement, with and without tensioned bow hair. Such computations are used with analytic models to model the admittance presented to the stretched bow hairs at the ends of the bow and to the string at the point of contact with the bow. Finite element computations are also used to demonstrate the influence of the lowest stick mode vibrations on the low frequency bouncing modes, when the hand-held bow is pressed against the string. The possible influence of the dynamic stick modes on the sound of the bowed instrument is briefly discussed.

Microwave conductivity and penetration depth in the heavy fermion superconductor CeCoIn5.

The electrodynamic properties of the quasi-two-dimensional heavy fermion superconductor CeCoIn5 have been investigated by microwave surface impedance measurements over a wide range of microwave frequencies and temperatures. We derive a value penetration depth lambda(0) approximately 190 nm, with a strong linear term in the temperature dependence of lambda(T) below T(c)/3, consistent with a superconducting gap with line nodes. The real part of the conductivity displays a broad peak at low temperatures consistent with a decreased scattering rate of almost 2 orders of magnitude below T(c). CeCoIn5 has remarkably similar properties to those of the high-T(c) cuprates.