The wavelength of air resonance in a tube depends on the length of the tube and the mode of resonance being considered. There are different modes of resonance that can occur in a tube, such as the fundamental mode (also known as the first harmonic) and higher harmonics.
For a tube that is open at both ends (open-closed tube), the fundamental mode has a wavelength equal to twice the length of the tube. In other words, the fundamental wavelength (λ₁) is approximately equal to 2L, where L is the length of the tube.
For a tube that is closed at one end and open at the other (closed-open tube), the fundamental mode has a wavelength equal to four times the length of the tube. In this case, the fundamental wavelength (λ₁) is approximately equal to 4L.
For higher harmonics or modes of resonance, the wavelengths are related to the fundamental wavelength (λ₁) by the ratio 1/n, where n represents the mode number or harmonic number. So, the wavelength of the nth harmonic (λₙ) can be expressed as λ₁/n.
It's important to note that these formulas assume idealized conditions, such as a tube with negligible diameter and the absence of end corrections. In reality, the presence of a tube diameter and end corrections can slightly affect the precise values of the wavelengths.
To calculate the exact wavelengths of air resonance in a specific tube, you would need to know the length of the tube and the mode of resonance (fundamental or higher harmonic) you are interested in.