Is knowledge of the physics governing brass instruments useful in their design and manufacture?

The short answer to the question posed in the title of this talk is, “Sometimes.” A successful example, which will be discussed in detail, started with the measured bore contour of an existing piccolo trumpet bell. A new contour was created by manipulating the so-called “Webster” horn equation. Several excellent players deemed the resulting instrument one of the two best piccolo trumpets available today. Other makers have used “bore optimization software” to improve the intonation of their instruments. However, there are still many unanswered questions about how brass instruments actually work in practice, and how the vocabulary players use describing tone quality, responsiveness, etc., relates to the physical world.