Which type of standing wave is the simplest that can be produced by a medium such as a guitar string?

The simplest type of standing wave produced by a medium, such as a guitar string, is known as the fundamental frequency. This fundamental wave is characterized by having the lowest frequency and the longest wavelength of all standing waves that can be formed in the medium. It occurs when the string vibrates in one segment, with the ends of the string fixed (e.g., at the bridge and the nut of the guitar).

In this configuration, the string can be visualized as vibrating in a single loop with a node at each end where there is no movement and an antinode in the center where the amplitude of the vibration is at its maximum. This fundamental mode of vibration serves as the foundation for creating higher harmonics or overtones, which are more complex standing waves that occur at integer multiples of the fundamental frequency. Understanding the fundamental frequency is crucial as it establishes the pitch of the note that is produced when the string is plucked or struck.