Section 9: On the Coexistence of Several Modes of Vibration in the Same Sounding Body

Abstract

Many or all of the modes of vibration that can be produced separately can coexist in the same sounding body; therefore, by listening with enough attention, one hears the sounds that correspond to all of these types of vibration. To get an idea of the changes in the shape of the elastic body, one must not apply the curvature that corresponds to a mode of vibration to the original shape of the body, but to the curvatures that already exist in each moment due to the other modes of vibration. Such a coexistence of many types of vibrations and many sounds is not necessary, as some have claimed, because in every mode of vibration where there are nodes, one can, by touching them or by applying a mute, exclude all types of vibrations in which these points should be moving, and produce the desired motion, and the sound that corresponds to it, without mixing in others.