©Toni Arregui
Before the 19th century, acoustics were based on the precepts of Anicius Manlius Severinus Boethius. He was a Roman scholar, philosopher and politician of the 5th–6th centuries. His works were the standard reference in Europe throughout the Middle Ages until the 18th century.
One of his books, De Institutione Musica, translated as The Fundamentals of Music, was the book for all matters concerning music. In this book, Boethius compares sound propagation to the propagation of water waves. Nowadays physics indeed encompasses both phenomena under mechanical wave propagation.
All musical instruments have a part that vibrates. That part can be strings, reeds, membranes, as well as other things, such as the lips of a trumpet player, and it is called the vibrating corpus. The vibration of the vibrating corpus produces mechanical waves in the actual substance of the instrument. These waves propagate, starting the propagation in the vibrating corpus itself. While propagating, those mechanical waves will repeatedly encounter the surfaces of the instrument. These surfaces, roughly speaking, are where the instrument ends and the air around and inside it begins; this boundary marks a change of density from a solid material to a gas. One part of those waves will be reflected on those surfaces, remaining in the substance of the instrument, and another part will get refracted through those surfaces into the air.
Thanks to their cavities (resonance boxes and the inside of pipes), musical instruments amplify the sound they produce, making it louder. This amplification occurs as follows: the air within the cavities receives waves of the same frequency from every refracting point. So, many waves coming from every direction get refracted into that same small amount of air inside the instrument, resulting in the superposition of all those waves—meaning that, while keeping their frequency, their peaks become higher and their troughs become deeper, which translates into a louder sound. Finally those amplified waves go out of the cavity through the holes of the resonance boxes and through the bottom and lateral holes of wind instruments.
In every instrument, the sound production process is exactly the same. The timbre of each instrument depends on the type, material, and shape of both the vibrating corpus and the whole instrument.
Sound is the translation that our brain does of the information perceived by our eardrums, the sensitive membrane of the aural system. What our eardrums perceive are mechanical waves. Normally we perceive these waves when they propagate through the air. These waves can also be perceived while they propagate through liquids, as whales and dolphins do in the ocean; or through solids: for instance, when a vibrating tuning fork is placed against your ear, or when a doctor examines you with a stethoscope.
The lack of answers from modern musical acoustics comes from the fact that acousticians don't think in terms of mechanical wave propagation to explain how musical instruments work; their theories come from another perspective. However, acoustics is a branch of physics, and one is expected to use mechanical wave propagation to study sound.
The problem acousticians have is that the sensors they use in their research do register mechanical waves, but then, filtering the collected data through their theories, acousticians don't interpret them as such—and so the conclusions they draw can only be incorrect. In fact, they are trying to explain how instruments work in a way that the builders of those instruments didn't know, because these theories only started to appear from sometime in the 19th century on—and, to make matters even more confusing, right around the time when the instruments were being transformed or had already been transformed to produce a louder sound.
©Toni Arregui