A bell lowers a tube’s cutoff frequency, easing high-frequency escape

Evidence

The treble boost argument goes like this: the bell assists sound in leaving the trumpet by smoothing the impedance transition to free air, and giving an effectively larger tube to radiate the sound (see figure 16.1). A cutoff frequency for a tube, whether it has a flare or not, or toneholes or not, is the frequency above which the reflections are weak. A bell lowers the cutoff frequency compared to a straight tube—that is, makes it easier for high frequencies to leave by releasing them from an effectively larger diameter. The treble boost idea is to let the higher frequencies out so that they can be heard, which seems simple enough. Most sources invoke this treble boost idea to explain the brilliance of a trumpet. The story is found most anywhere musical acoustics is explained. — Eric J. Heller, Why You Hear What You Hear- An…, 1506

Categorization

• DEFINE: Clarifies cutoff frequency as the threshold above which reflections are weak, and how a flare lowers it.
• XREF: connects to: The bell reflects low frequencies deep inside and high ones near its rim — David Howard, Jamie Angus, coustics and Psychoacoustics, 1272