Minimal impedance horns must expand exponentially in diameter

Evidence

Within the lumping picture and according to the geometric mean principle, we can show that minimizing the impedance requires that the diameter of the tube should increase exponentially. — Eric J. Heller, Why You Hear What You Hear- An…, 553

Categorization

• XREF: Connects to exponential taper discussions in loudspeaker and brass-instrument acoustics texts; the geometric mean principle reprises impedance matching themes from earlier chapters.
• QUESTION: Does the exponential horn shape also hold for practical instruments like brass horns, which are not exponential?
• corroborated: 2 independent passages support this claim — Eric J. Heller, Why You Hear What You Hear- An…, 553