Which formant frequency corresponds to the odd multiples in the quarter wave resonator theory?

In the context of the quarter wave resonator theory, which is often used to describe the acoustic properties of certain vocal tract shapes, the correct answer identifies that only odd multiples of the fundamental frequency correspond to the resonant frequencies of the system.

A quarter wave resonator is defined such that one end is closed (like the larynx in human speech) and the other end is open (like the mouth). This configuration allows for resonance at wavelengths that fit a quarter of the wavelength within the length of the resonator. Consequently, the resonant frequencies are determined by the odd harmonics; the first harmonic, or the fundamental frequency, corresponds to the first odd multiple (1x), while the next resonances occur at 3x and 5x, and so on.

This principle is fundamental in speech science to understand how different vowel sounds are produced and how they resonate within the vocal tract. The focus is on these odd multiples because they align with the quarter-wave pattern fitting correctly into the shape of the resonator, thereby enhancing certain frequencies that are crucial for vocal quality and speech clarity. Thus, identifying "only odd multiples" as corresponding to the formant frequencies accurately reflects the nature of resonant frequencies produced in a quarter wave reson