In acoustics we meet with the case where a body is urged towards a fixed point by a force varying as the distance, and is also acted upon by an extraneous or disturbing force which is a given function of the time.
In acoustics his principal work was a research on the transmission of sound through solids, the explanation of Chladni's figures of vibrating solids, various investigations of the principles of acoustics and the mechanism of hearing, and the invention of new musical instruments, e.g.
The efforts which were consequently made in the early days of spectroscopy to discover some numerical relationship between the different wave lengths of the lines belonging to the same spectrum rather disregard the fact that even in acoustics the relationship of integer numbers holds only in special and very simple cases.
Barnes, Practical Acoustics (1898), treats the subject experimentally.
In acoustics he invented, about 1819, the improved siren which is known by his name, using it for ascertaining the number of vibrations corresponding to a sound of any particular pitch, and he also made experiments on the mechanism of voice-production.
The theory of proportion, and the study of acoustics and music were considerably advanced by his investigations.
They were written at the request of the princess of Anhalt-Dessau, and contain an admirably clear exposition of the principal facts of mechanics, optics, acoustics and physical astronomy.