A natural frequency, also called a resonant frequency, is the frequency at which an object vibrates when struck, plucked, strummed or otherwise disturbed. All objects have one or more natural frequencies, which are dependent upon the object's size, shape and the properties of the materials of which it is made.
If the amplitude of the vibrations is sufficiently large and if the natural frequency is within the range of human hearing (roughly 20 to 20,000 Hz, depending on the individual), then the vibrating object will produce audible sound waves. The timbre of the sound depends on the specific mixture of natural frequencies of the object and their respective intensities.
The natural frequency of some objects, such as a tuning fork and a flute, is almost completely a single frequency and thus results in a pure tone. Most musical instruments have a set of natural frequencies that are mathematically related by whole number ratios, which results in a rich tone. Other objects, such a a shoe or cup or door, when dropped on the floor or struck or slammed, produce a complex set of frequencies that have no simple mathematical relationship to each other, and thus the resulting sounds are not musical but, rather, are described as noise.