The piano is a complex musical instrument consisting of several components influencing vibration and sound production. By understanding the sound production mechanism virtual instruments can be created (physics-based sound synthesis) and the design and manufacturing of soundboards can be supported (virtual prototyping). Based on previous results published in the literature, a piano model was built and extended by a near field sound radiation model capable for physics-based sound synthesis. In this paper a simplified piano model is presented, including hammer strike and hysteretic felt models, coupled lossy string model and a 2D FEM based stiffened plate model for soundboard. This paper contains a parametric study where the soundboard parameters, such as its material characteristics and boundary conditions, are modified and their effect on the soundboard's modal behavior and the radiated sound is analyzed. Instead of using only musical (qualitative) descriptors, e.g. brightness or coloring, the piano sounds are characterized based on standard quantitative descriptors (e.g. harmonic ratio, spectral centroid). It is shown that these descriptors are determined by soundboard admittance, string characteristics and position on the soundboard; radiated sound from wooden soundboards can be characterized as harmonic for wide range of initial material descriptors; the string position is essential, and the perceived sound can differ significantly for different listening positions, even for the same harmonic decay pattern.