Longitudinal vibration of piano strings greatly contributes to the distinctive character of low piano notes. In this paper a simplified modal model is developed, which describes the generation of phantom partials and longitudinal free modes jointly. The model is based on the simplification that the coupling from the transverse vibration to the longitudinal polarization is unidirectional. The modal formulation makes it possible to predict the prominent components of longitudinal vibration as a function of transverse modal frequencies. This provides a qualitative insight into the generation of longitudinal vibration, while the model is still capable of explaining the empirical results of earlier works. The semi-quantitative agreement with measurement results implies that the main source of phantom partials is the transverse to longitudinal coupling, while the string termination and the longitudinal to transverse coupling have only small influence. The results suggest that the longitudinal component of the tone can be treated as a quasi-harmonic spectrum with formantlike peaks at the longitudinal modal frequencies. The model is further simplified and applied for the real-time synthesis of piano sound with convincing sonic results.
The effect of irradiance during low temperature hardening was studied in a winter wheat variety. Ten-day-old winter wheat plants were cold-hardened at 5 ∞C for 11 days under light (250 μmol m Ð2 s Ð1 ) or dark (20 μmol m Ð2 s Ð1 ) conditions. The effectiveness of hardening was significantly lower in the dark, in spite of a slight decrease in the F v /F m chlorophyll fluorescence induction parameter, indicating the occurrence of photoinhibition during the hardening period in the light. Hardening in the light caused a downshift in the far-red induced AG (afterglow) thermoluminescence band. The faster dark re-reduction of P700 + , monitored by 820-nm absorbance, could also be observed in these plants. These results suggest that the induction of cyclic photosynthetic electron flow may also contribute to the advantage of frost hardening under light conditions in wheat plants.
This paper presents a new nonlinear least-squares algorithm for fitting band-limited periodic signals with unknown frequency and harmonic content. The new solution features a model-based recursive calculation method that requires less memory space and has smaller computational demand than the known matrix-based algorithms.
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