Finger-hole diameters determine where a pipe’s effective opening lies

Evidence

Players are able to play a number of different notes on the same instrument by changing the effective acoustic length of the resonator. This can be achieved, for example, by means of the sliding piston associated with a swanee whistle or, more commonly, when particular notes are required, by covering and uncovering holes in the pipe walls known as “finger holes.” A hole in a pipe will act in an acoustically similar manner to an open pipe end ( pressure node, velocity antinode). The extent to which it does this is determined by the diameter of the hole with respect to the pipe diameter. When this is large with respect to the pipe diameter, as in the flute, the uncovered hole acts acoustically as if the pipe had an open end at that position. Smaller finger holes result acoustically in the effective open end being farther down the pipe (away from the flue end). This is an important factor in the practical design of bass instruments with long resonators, since it can enable the finger holes to be placed within the physical reach of a player’s hands. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1187

Categorization

• DEFINE: Explains the acoustic principle linking finger-hole size to effective pipe end position.
• XREF: Connects to practical instrument design constraints in the reader’s acoustics study. — connects to: Nicking the pipe edges smooths onset and suppresses high-frequency components; Multiple open holes jointly shift the effective pressure node; Tone-hole fingering requires modes to keep constant frequency ratios as holes open (+4 more)
• corroborated: 2 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1187

Broader Connections

• Multiple open holes jointly shift the effective pressure node #expands (0.85)
• A mouthpiece’s popping frequency reveals how it extends effective pipe length. #expands (0.82)
• Tone-hole fingering requires modes to keep constant frequency ratios as holes open #qualifies (0.78)
• Open pipe ends reflect low frequencies but pass high frequencies #expands (0.75)
• Open tube ends preferentially reflect long wavelengths and let short ones escape #expands (0.75)