Which dimensionless number is source speed divided by local sound speed?

Which dimensionless number is source speed divided by local sound speed? It is the Mach number. In its usual aerodynamic form, Mach number is the ratio of an object’s speed to the local speed of sound: M = v/a, where v is the object’s speed and a is the medium’s local sound speed.

The number has no units because it compares two speeds. Mach 1 means the object is traveling at the local speed of sound; Mach 2 means twice that speed. “Local” matters because sound speed changes with temperature, composition, and other properties of the medium, especially in the atmosphere.

Mach number is named for physicist and philosopher Ernst Mach, whose work on supersonic motion helped establish the terminology. Around Mach 1, compressibility effects become especially important, and shock waves can form. Subsonic flow is generally below Mach 1, while supersonic flow is above it; hypersonic flow is commonly associated with Mach 5 and higher.

Mach number is not a measure of speed alone. The same vehicle speed can correspond to different Mach numbers at different altitudes or temperatures because the local sound speed changes. It also differs from Reynolds, Froude, and Prandtl numbers, which compare other physical effects.