International Symposium on Musical Acoustics (ISMA-02), Mexico City , 2002, http: //www.acoustics.hut.fi/~cerkut/publications. html . 124 C. Erkut and M. Karjalainen, ``Virtual strings based on a 1-D FDTD waveguide model,'' Proceedings of the Audio Engineering Society 22nd International Conference, Espoo, Finland , pp. 317-323, June 15-17, 2002, http: //www.acoustics.hut.fi/~cerkut/publications. html . 125 P. A. A. Esquef, M. Karjalainen,