Ideal vibrations of a continuum are described by a partial differential equation and that this contains an infinite number of ordinary differential equations defining the spatial configurations of the vibrating media. These spatial configurations are called modes and they are often best understood through their nodes or nodal structure. Explain the meaning of the above statement. What is vibrating? How are these vibrations realized, e.g., touch, sight, hearing, etc.? What is a mode of the continuum? Does the spatial mode have nodes? If so, then what are they?

Ideal vibrations of a continuum are described by a partial differential equation and that this contains an infinite number of ordinary differential equations defining the spatial configurations of the vibrating media. These spatial configurations are called modes and they are often best understood through their nodes or nodal structure. Explain the meaning of the above statement. What is vibrating? How are these vibrations realized, e.g., touch, sight, hearing, etc.? What is a mode of the continuum? Does the spatial mode have nodes? If so, then what are they?