Confining reflected sound can radiate more power than an open bell on resonance.

Evidence

Trumpets rely on resonance, and resonance relies on reflection and confinement. In the absence of friction and dissipation, there is no contest: on resonance letting out the sound is self-defeating and makes it less loud (a trumpet is played on resonance). A Ripple check on this is shown in figure 16.18, by comparing the cases of an added bell to an added constriction, a kind of anti-bell. Both were driven from the left by the same source of wave amplitude. There are very weak resonances near the frequency used if a bell is present, and strong resonances for the constricted anti-bell. On or near resonance, the anti-bell, which reflects high-frequency partials, is much louder outside than is the pipe with a bell. Of course, between resonances the power is much less from the anti-bell, such that the power averaged over frequency intervals spanning a few resonances is the same as with a bell present (the average power theorem). There is no friction in this simulation, so more confinement leads to more sound radiation, shown by the dashed line in figure 10.10. We will add wall friction to the discussion momentarily—it is essential. — Eric J. Heller, Why You Hear What You Hear- An…, 1513

Categorization

• XREF: Directly connects to chapter 10’s discussions of sound production competing with damping and the average power theorem.
• DEFINE: Introduces ‘average power theorem’ — that time-averaged radiated power is independent of confinement.