Fat pipes vs thin pipes: why does the pitch of a fat pipe of an organ depend more on the blowing pressure?
The reflection at the open end of a pipe depends on the ratio of the wavelength to the radius of the pipe. For the same wavelength, the reflection coefficient is higher for a narrow pipe than for a wide. The greater the reflection, the stronger the resonance, and the smaller the band of frequencies for which it will occur. Consequently, the resonance of a narrow pipe is also narrow: a narrower band of frequencies will cause resonance in a narrow pipe than in a wide pipe of the same length. Consequently, one can ‘bend’ the note more on a wide pipe: one can drive it at a frequency further from its resonance.
