Acoustic normal modes below 4 kHz for a rigid, closed violin-shaped cavity

Abstract

Numerical calculations of standing wave patterns ≤4 kHz in a closed (no f-holes), rigid, violin-shaped cavity excited by a movable point source were used to investigate internal resonant pressure mode shapes. Approximate normal mode shapes were extracted by appropriate choice of excitation point and tested for orthogonality. Excellent agreement was found with published experimental mode shapes and frequencies below 2 kHz, and with mode frequencies up to 4 kHz when no mode shapes were available. Calculations performed without the end and corner blocks (interior outline same as exterior) from 0.4–4 kHz showed little sensitivity of mode frequency and shape to this cavity shape change. The frequency f(A1) of the lowest closed cavity mode A1 at ∼490 Hz was observed to decrease by 24 Hz when the arch was reduced to zero (flat top and back plate) with rib height held constant. On the other hand when the rib height was reduced (arch still zero), f(A1) increased, but more slowly. The effects of arch and rib height changes are consistent with experimental data from actual instruments for the A1 mode.