The extent of the fluid, agitated by the two opposite oscillations of the solid plane, is what we call the breadth of an _entire undulation_, and we may consequently give the name of _semiundulation_ to each of the parts actuated by the opposite undulations; the whole constituting a _complete oscillation_, since it comprehends the return of the vibrating plane to the initial situation. It is obvious, that the two semiundulations, which compose the complete undulation, exhibit, in [p120] the fluid strata which they contain, velocities absolutely equal in magnitude, but with contrary signs, that is to say, carrying the particles of the fluid in opposite directions. These velocities are the greatest in the middle of each of the semiundulations, and decrease gradually towards their extremities, where they entirely vanish: so that the points of rest, and of the greatest velocities positive and negative, are separated from each other by intervals of one fourth of an undulation.
The length of an undulation, _d_, depends on two things: first, on the promptitude with which the motion is propagated in the fluid; and secondly, the duration of the complete oscillation of the vibrating plane; for the longer this duration, and the more rapid the propagation of the motion, the greater will be the distance to which the first agitation has been extended at the instant of the return of the solid plane to its initial situation. If the oscillations are all performed in the same medium, the velocity of propagation remaining the same, the length of the undulations will be simply proportional to the duration of the oscillations of the vibrating particles from which they originate. As long as the vibrating particles continue to be subjected to the same forces, it follows from the principles of mechanics that each of their minute oscillations will occupy the same time, whatever their extent may be; so that the corresponding undulations of the fluid will continue to be of the same length; they will only differ from each other in the greater or less extent of the elementary vibrations of the particles, which will be proportional to the extent of the luminous particles; for it appears from what has already been stated, that each stratum of the fluid repeats exactly all the motions of the vibrating particle. The greater or less amplitude of the oscillations of the strata of the fluid determines the degree of absolute velocity with which they move, and consequently the energy, but not the nature of the sensation which they excite, which must depend, according to every analogy, upon the duration of the oscillations. It is thus that the nature of the sounds, transmitted by the air to our ears, depends entirely on the duration of each of the oscillations executed by the air, or by the sonorous [p121] body which puts it in motion; and that the greater or less amplitude or energy of the oscillations only augments or diminishes the intensity of the sound, without changing its nature, that is, its tone, or pitch.