The speed of sound in gases is derived in a manner similar to what was done for the speed of waves on a string. The mass of the gas molecules provides the inertial contribution. The gas laws, along with approximation techniques, are used to estimate the return force. The appropriate process is adiabatic, and so the speed of sound depends on the adiabatic constant. The adiabatic constant, in turn, depends largely on the shape of the molecules. Excellent agreement is found between the rather simple theory and measured results. The speed of sound in a gas is found to depend on the (average) mass of the molecules, temperature, and the adiabatic constant (the shape of the molecules); however, there is very little pressure dependence when the pressure is near 1 atmosphere.

This chapter introduces influence of density change on a flow, i.e., the compressible flow theory. Strictly speaking, any gas flow is both viscous and compressible. In tradition the influence of viscosity and compressibility are dealt with separately to make things easy. In this book, the chapter 6 deals with viscosity, and the chapter 7 deals with compressibility. Sound speed and Mach number are introduced in the beginning, then the equations for steady isentropic flow are derived with statics and total parameters introduced. Some gas dynamic functions are derived that use coefficient of velocity in replace of Mach number. Propagation mode of pressure waves are discussed next, and expansion and compression waves are introduced. Shock wave, as a strong compression wave, is discussed in depth. In the end, transonic and supersonic flow in a variable cross-section pipe is discussed, especially the characteristics of the flow in a Laval nozzle.