Several experiments have been performed to investigate the mechanical vibrations associated with an organ pipe. The measurements have been made by using laser Doppler vibrometry, a well-known not-invasive optical measurement technique that is very widely used in structural dynamics. The recorded signals are analyzed by using a well-established decomposition method in time domain, i.e., independent component analysis. Asymptotic dynamics methods to recognize low-dimensional dynamic system associated with this wave field is then considered. The full-toned recorded signals appear decomposed into three independent components. The independent components are nonlinear due to the fractal dimension of the attractor. These results for the mechanic vibrational field are compared with those of the acoustic one. It is interesting to note that the two fields have many common characteristics. Finally, a low-dimensional dynamic system that reproduces the main characteristics of the mechanical wave field in the time and frequency domains is introduced.