When you blow air through a long tube, the wavelength and frequency of the sound produced can be affected.
In a closed tube, such as a flute or a clarinet, the air column inside the tube can resonate and produce specific frequencies or pitches. The length of the tube determines the fundamental frequency or the lowest resonant frequency that can be produced. The longer the tube, the lower the fundamental frequency.
When you blow air into the tube, it creates vibrations in the air column, causing it to resonate at specific frequencies. The wavelength of the sound produced is determined by the length of the tube and the harmonic produced. The fundamental frequency corresponds to the first harmonic, where the wavelength is approximately four times the length of the tube. As you increase the blowing pressure or change the finger positions (in the case of instruments with keys or holes), the higher harmonics are produced, resulting in shorter wavelengths and higher frequencies.
In an open tube, such as a flute with an open end, the air column can also resonate. However, the fundamental frequency for an open tube is determined by the length of the tube and is approximately twice that of a closed tube of the same length. The open end allows for the displacement of air particles, which affects the resonance pattern.
In summary, when you blow air through a long tube, the length of the tube determines the fundamental frequency, and the blowing pressure and finger positions (for certain instruments) can alter the harmonic produced. The wavelength and frequency of the sound produced depend on these factors and the characteristics of the tube, whether it is open or closed.