the fundamental frequency
When a guitar string or an organ pipe sounds a note, the pitch you name, that A or that C, is its lowest and strongest tone. That lowest natural frequency is the fundamental frequency. The question it answers is: of all the tones a string can make, which one do we call its note?
The fundamental frequency f_1 is the lowest frequency at which a system forms a standing wave, its simplest vibration pattern, with the fewest nodes. Every other harmonic is a whole-number multiple of it (f_n = n f_1). For a string fixed at both ends, or a pipe open at both ends, the simplest pattern fits half a wavelength into the length L, giving f_1 = v / (2L). For a pipe closed at one end, only a quarter-wavelength fits, so f_1 = v / (4L).
The fundamental sets the perceived pitch, while the higher harmonics colour the sound. This is why a shorter string or pipe plays higher (smaller L means bigger f_1), and why tightening a string (which raises the wave speed v) sharpens its pitch, the physics behind tuning any string instrument. An honest note: our ear often assigns pitch to the fundamental even when it is weak or missing, reconstructing it from the spacing of the harmonics.
An organ pipe open at both ends and 0.5 m long, with sound speed v about 343 m/s, sounds a fundamental f_1 = v/(2L) = 343/(2 times 0.5) = 343 Hz.
The fundamental is the lowest standing-wave frequency, f_1 = v/(2L) for a string fixed at both ends.
The fundamental is the 1st harmonic. Shortening the string or pipe, or speeding up the wave, raises it, which is the basis of tuning and of fingering notes.