Beamformer-based estimation of longitudinal wave speed in tonewood

Mechanical properties of the wood have great impact on the design of musical instruments. As a matter of fact, luthiers accurately select tonewoods according to some desired elastic features. Typically, their choices are based on the longitudinal wave speed. In order to avoid direct parameter estimation techniques which can bring wood specimens to rupture, either empirical rules of thumb or expensive equipment with high sampling frequency are customarily employed. In this paper we propose a methodology for speed estimation starting from impulse responses acquired by accelerometers placed at the block edges. The technique relies on the definition of the Delay And Sum (DAS) beamformer, where instead of steering the beamformer to different Directions of Arrival (DOAs), we evaluate the filter output varying the wave speed. The proposed method is non-invasive, low-cost and it requires only basic expertise on hammer testing. We assessed the accuracy of the estimation using both simulated signals and measures on actual tonewoods. We compared the resulting performance with that of another state-of-the-art technique working at the same sampling frequency and with the same setup. Results show the effectiveness of the beamformer also in the case of low sampling frequency and high speeds.