Very good reference Edward. Everyone needs to read it.

If you go to Edward's reference site

https://www.aerospaceweb.org/question/atmosphere/q0126.shtml
you will see that the speed of sound depends only on the local temperature of the air and the composition of the air (through the ratio of specific heats which for sea level altitudes means slight differences in the humidity levels).

From the above reference.

"...the speed of sound is not a single value, but changes with altitude. To be more precise, the speed of sound (a) can be directly calculated based on the air temperature (T), and temperature is a function of altitude. A procedure for calculating the temperature, as well as the density and pressure, using the standard atmosphere model was described in a previous question (learn more). Towards the end of that explanation, an equation for calculating the speed of sound based on temperature is also introduced. This equation is based on the more general form

a= sqrt( g R T )

where

a = speed of sound [ft/s or m/s]

g = specific heat ratio, which is usually equal to 1.4 (for dry air)

R = specific gas constant, which equals 1716 ft-lb/slug/°R in English units and 287 J/kg/K in Metric units

T = atmospheric temperature in degrees Rankine (°R) in English units and degrees Kelvin (K) in Metric units

Once the speed of sound is known, the Mach number can be easily computed by dividing the airspeed of the vehicle by the speed of sound.

... The Mach number (M) is simply the ratio of the vehicle's velocity (V) divided by the speed of sound at that altitude (a).

M = V / a. "

Now to correct some misconceptions presented in the thread.

r1dermon

There is no "sound barrier" and the generation of sonic booms is well understood.

When a rocket exeeds the speed of sound, it is the the interaction of the surrounding air that changes. Instead of simply compressing the air in front of it, the rocket generates a shock wave. The subsonic air compression interaction in front of a rocket is themodynamically reversible where as the supersonic air compression is not.

phaar

A sonic boom is always generated anytime an object goes supersonic. To hear it you have to be in the right place.

A small object shocks a relatively small volume of air, and the shock wave get weaker and slower as it travels away from the rocket. At some point, the wave slows down to the speed of sound and becomes a simple sound wave. All sound waves travel at the local speed of sound as calculated from the equation above. The intensity of any sound wave decreases as 1/D<sup>2</sup> (distance squared) from the source and at some point is too weak to be heard.

You do not need to glass a rocket that will exceed Mach 1. Again there is nothing magical about it. As it always the case, the total load on your rocket equals the instantaneous thrust of the motor. Sustained Mach flight places certain thermal constraints on the vehicle skin becase of the loss of strength due to aerodynamic heating, but this not an issue for model and most high power rockets.

There is no cyclonic cloud formed due to a shock wave. I think you probably referring to the spectacular video of the Navy jet traveling a Mach 1 near a carrier at sea level and have observed the formation of a conical condensation cloud caused by the expansion and cooling of the air after the shock wave has passed.

Bob Krech