Doubling all pipe dimensions lowers its fundamental tone by an octave

Evidence

Similarity explains the law discovered first by Mersenne, that a pipe twice the length of another has a fundamental mode an octave down. Low-frequency pipe modes are uniform across the diameter of the pipe, so scaling in that direction doesn’t matter very much. However, a refined statement is that all three dimensions of the pipe should be scaled, and if by a factor of 2, the fundamental note will go down by almost exactly an octave. In this case, the impedance mismatch at the open end and even the end corrections have been properly scaled, whereas if only the long direction is scaled, reflection amplitude at the end and the end correction are somewhat different for the two pipes. — Eric J. Heller, Why You Hear What You Hear- An…, 600

Categorization

Category: Causal Relationships

Related

• Pipe length sets pitch while diameter and material shape harmonic strength (similarity 0.86)
• An open pipe’s fundamental period equals twice its length divided by wave speed (similarity 0.84)
• Wide pipes are weak in upper harmonics (similarity 0.82)
• Any pipe diameter change causes partial sound reflection at the junction (similarity 0.82)
• Wide organ pipes suppress upper harmonics in their output (similarity 0.82)
• Narrower pipes raise acoustic impedance through in-phase wall reflections (similarity 0.82)
• Pipe diameter changes reflect pressure pulses with opposite sign (similarity 0.81)
• A stopped pipe sounds an octave lower than an open pipe of equal length (similarity 0.81)
• Open pipe ends invert pulse polarity while closed ends preserve it (similarity 0.81)
• Overblowing a pipe jumps its pitch to the next resonator-supported harmonic (similarity 0.79)
• An open-open pipe’s modes form a complete harmonic series at integer multiples (similarity 0.78)
• An open pipe end inverts a sound pulse’s sign via a reflected rarefaction (similarity 0.78)
• Raising airflow or lowering the cut-up makes flue pitch jump discontinuously (similarity 0.78)
• Adding a mouthpiece lowers higher modes more than lower ones. (similarity 0.78)
• Resonator length and end condition alone determine flue pipe pitch (similarity 0.78)

Broader Connections

• Pipe length sets pitch while diameter and material shape harmonic strength #expands (0.80) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1182