End Conditions of Piano Strings

The end conditions of piano strings can be approximated by the input admittance at the bridge. Proper measurements of this value are therefore required. A method of validation of admittance measurements on simple structures is proposed in this paper. High resolution signal analysis performed on string’s vibrations yields an estimate for the input admittance. This method is implemented on a simplified device composed of a piano string coupled to a thin steel beam. INTRODUCTION The research of a trade-off between loudness and sustain (duration) is a major issue for piano designers and manufacturers. The way the energy of vibration is transferred from the piano string to the soundboard depends on the end conditions of the strings at the bridge: these conditions can be approximated by the input admittance at the connecting point between the string and the resonator. Therefore, proper measurements of this value are needed. Given this, we propose here a method of validation of admittance measurements on simple structures. Parameters such as frequencies and damping factors of the string partials depend directly on the end conditions. The analysis of the vibratory signal of the string, based on high resolution estimation methods (ESPRIT algorithm), allows us to evaluate efficiently those parameters and leads to the calculation of the input admittance. This method is implemented on a simplified device composed of a piano string coupled to a thin steel beam. The comparative study of two experimental cases (isolated string vs. coupled string) leads us to the input admittance. This value, derived from vibratory measurements of the string is compared to direct admittance measurements performed on the beam, and to theoretical predictions, in order to validate the method. STRING-SOUNDBOARD COUPLING IN PIANOS Summary of piano acoustics The vibrations of the piano string are coupled to the soundboard (which radiates the sound) via the bridge (Figure 1). This coupling determines the tone duration and the sound power. The boundary conditions of the string must ensure a compromise between sound power efficiency (high transverse velocity for a given string force) and tone duration (low soundboard velocity). ha l-0 05 58 48 7, v er si on 6 18 O ct 2 01 2 Author manuscript, published in "International Symposium on Musical Acoustics, ISMA 2007, Barcelona : Spain (2007)"