I found this book very helpful. It presents the subject in a very clear step by step manner with many lucid examples. It contains no advanced math, but it still scientifically presents some complicated acoustics, using instead insights gained from years of research, teaching, and working with musicians and their instruments. He assumes little background and builds all his explanations up from very basic physical concepts. It is true, however, that his thoroughness with this approach occasionally demands some patience. Though the book was written in the mid '70s, most of the material is unhindered by the passage of time. Many of the figures are very simply drawn (low-tech), but they are nonetheless remarkably clear and understandable.
I have found this book a good complement to "The Physics of Musical Instruments" by Fletcher and Rossing. Benade's book is easier to read and understand (and much less expensive). Fletcher and Rossing, on the otherhand, have written an excellent college physics book, which is exceptionally detailed and covers a wide variety of basic phenomena and instruments. They rely much more on math to explain the subject, instead of using the practical, anecdotal approach of Benade. The two different approaches work well side by side. If I were to buy just one book, however, I'd buy Benade's.