The sealed end must remain a displacement node, while the open end must remain a displacement antinode. These boundary conditions permit a quarter-wavelength pattern at the fundamental and additional patterns formed by adding two quarter-wavelength segments at a time. As a result, resonances occur at the fundamental and its odd multiples, while even harmonic patterns do not satisfy both ends simultaneously.
A resonant wavelength must fit the tube so that a displacement node occurs at the sealed boundary and an antinode occurs at the open boundary. The shortest allowed pattern contains one quarter of a wavelength within the tube. Longer allowed patterns contain three, five, or other odd numbers of quarter-wavelengths, producing the sequence of permitted resonances.
Increasing the tube length increases the wavelength required for the fundamental standing-wave pattern, so the fundamental frequency decreases when the speed of sound remains unchanged. Shorter tubes produce shorter fundamental wavelengths and higher frequencies. This length dependence makes the system useful for examining how physical dimensions control acoustic pitch and resonance.
For a given tube length, the speed of sound determines how quickly the resonant wavelength corresponds to an oscillation in time. A higher sound speed produces higher resonant frequencies for the same allowed wavelength, whereas a lower speed produces lower frequencies. Consequently, resonance measurements connect the tube’s dimensions with wave propagation in air.
A laboratory investigation can compare tube length with the quarter-wavelength condition and identify the fundamental resonance and successive allowed resonances. By examining how those frequencies change as the tube length changes, students can test the predicted dependence on length and distinguish the odd-harmonic pattern from the full set of possible harmonic frequencies.
Organ pipes and clarinets provide practical examples in which an air column produces pitch through standing-wave resonance. Their acoustic behavior can be interpreted using the node at a closed boundary, the antinode at an open boundary, and the resulting odd-harmonic series. The closed-open tube model therefore links laboratory wave studies with the production of musical sound.