What is defined as the lowest frequency of vibration of a standing wave?

The correct answer is fundamental frequency, which refers specifically to the lowest frequency produced by a standing wave in a vibrating medium. In the context of music and acoustics, the fundamental frequency serves as the primary pitch or tone that is perceived when a musical instrument is played. It is the frequency at which the entire system vibrates and is the foundation upon which higher frequencies, known as harmonics or overtones, are built.

Understanding the fundamental frequency is crucial because it dictates the overall sound quality (timbre) of the instrument. When a string, air column, or any other medium vibrates, it can create multiple frequencies simultaneously, but the fundamental frequency is the lowest and most dominant one.

In contrast, harmonic frequencies are integer multiples of the fundamental frequency and create the richer sound (harmonic series). Resonant frequency refers to the specific frequencies at which a system naturally oscillates, which can sometimes coincide with the fundamental frequency but could also be at other levels depending on the system's characteristics. Overtones are higher frequencies that occur above the fundamental and contribute to the tonal richness of the sound but are not the lowest frequency themselves.