Final answer:
The resonant frequency is the frequency at which an object naturally oscillates the most, and it is synonymous with its lowest-frequency resonance or fundamental frequency. Overtones are higher frequencies, and together with the fundamental, they form harmonics.
Step-by-step explanation:
The resonant frequency of an object refers to the frequency at which the object naturally oscillates with the greatest amplitude due to resonance. It is the frequency at which an object is the most prone to vibration when exposed to an external force or a matching frequency. The term 'fundamental frequency' is often used interchangeably with 'resonant frequency', but to be precise, it specifically describes the lowest-frequency resonance of an object. All other higher resonant frequencies are known as overtones. Together, the fundamental frequency and its overtones are termed harmonics, where the fundamental frequency is the first harmonic, and the subsequent overtones are the second, third harmonics, etc.
These concepts are incredibly important for understanding the behavior of sound in various mediums, such as the distinct sounds produced by different musical instruments. For instance, whether an instrument uses air columns, strings, sounding boxes, or drumheads, it is the mix of the fundamental frequency and overtones that give it its unique timbre. Moreover, the same principles apply to various physical systems beyond sound, such as resonant frequencies found in the standing waves of vibrating strings and the wave characteristics of electrons in atoms.