Mach number = TAS/ Local speed of
sound (LSS)
LSS is proportional to the SQRT of
the absolute temperature. Temp goes up LSS goes up. Temp down LSS goes down.
A shock wave is formed as a number of
pressure waves come together this results in an increase in pressure and
temperature, therefore the LSS increases in a shock wave. Shock waves reduce
the velocity of airflow through them. So in respect to the mach number of an airflow it reduces through a shock wave. Through a normal
shock the flow will always reduce to below Mach 1. In an oblique shock it will
still be at mach 1 or above but lower than the mach no of the flow going into
the shock wave
In an expansion wave, as the name
suggest the air is expanding this reduces pressure and temperature and so LSS
goes down. As the air expands it increases in velocity. So TAS goes up LSS goes
down so Mach no increases.