The historical connections between physics and music are discussed, and the questions “What is music?” and “What is physics?” are addressed. The area of overlap is presented as the topic for the remainder of the book. The use of numbers having limited accuracy, identified with units and possibly other qualifiers, to specify quantities measured by physicists is presented. Scientific notation and unit prefixes are reviewed.

Sound in one-dimensional systems, pipes, is considered in the context of modeling of the physics of wind instruments. Acoustic impedances are defined, which are used to characterize a system’s response to a force. The convenience of using complex numbers, which have real and imaginary parts, to describe impedance for waves, which have an amplitude and phase, is presented. Reflection and transmission of sound at points where a pipe’s impedance changes are considered, along with how these lead to resonances. The differences between sound propagation in cylindrical, conical, and Bessel horn-shaped pipes are presented. A model pipe with periodic holes is used to model the finger holes found in woodwinds. Such a pipe exhibits a critical frequency below which the impedance is imaginary, resulting in reflection, and above which is real-valued, allowing sound to propagate. An explicit example is shown using simple calculations for a fife, illustrating that the critical frequency becomes important for the upper range of woodwinds. A solution method for more advanced pipe models is presented. One more advanced model is that used for the human vocal tract, which can be modeled with pipes and acts as a time-dependent filter.

This chapter discusses two different approaches to describing fluid flow: a Lagrangian approach (following a fluid element as it moves) and a Eulerian approach (watching fluid pass through a fixed volume in space). Understanding each of these descriptions of flow is needed to fully understand the dynamics of fluids. This chapter is devoted to diving into the differences between the two descriptions of fluid motion. Understanding this chapter will help tremendously in the understanding of the upcoming chapters when the Navier–Stokes equations and energy equation are discussed. This chapter will introduce the material derivative. It is extremely important to understand this derivative before the Navier–Stokes equations themselves are tackled.

In the previous chapter, the forces acting on a moving fluid element were exhaustively studied. Using Newtons second law of motion, the Navier–Stokes equations for both compressible and incompressible flows were obtained. This chapter uses an alternative approach to developing the Navier–Stokes equations. Namely, by starting from a Eulerian description (as opposed to a Lagrangian description), the integral form and conservation form of the Navier–Stokes equations are developed. The continuity and Navier–Stokes equations in its various forms are tabulated and reviewed in this chapter. This chapter ends by solving some very simple, yet common, problems involving the incompressible Navier–Stokes equations.

This chapter develops the Navier–Stokes equations using a Lagrangian description. In doing so, the concept of a stress tensor and its role in the overall force balance on a fluid element is discussed. In addition, the various terms in the stress tensor as well as the individual force terms in the Navier–Stokes equations are investigated. The chapter ends with a discussion on the incompressible Navier–Stokes equations.

This chapter serves as an introduction to the concept of conservation and how conservation principles are used in fluid mechanics. The conservation principle is then applied to mass and an equation known as the continuity equation is developed. Various mathematical operations such as the dot product, the divergence, and the divergence theorem are introduced along the way. The continuity equation is discussed and the idea of an incompressible flow is introduced. Some examples using mass conservation are also given.

In this chapter, a concept known as scaling is introduced. Scaling (also known as nondimensionalization) is essentially a form of dimensional analysis. Dimensional analysis is a general term used to describe a means of analyzing a system based off the units of the problem (e.g. kilogram for mass, kelvin for temperature, meter for length, coulomb for electric change, etc.). The concepts of this chapter, while not entirely about the fluid equations per se, is arguably the most useful in understanding the various concepts of fluid mechanics. In addition, the concepts discussed within this chapter can be extended to other areas of physics, particularly areas that are heavily reliant on differential equations (which is most of physics and engineering).