Thanks to all for your replies. It is starting to make a little more sense. I really tried to do some research on this subject, but have had a little difficulty in putting it all together. Here is another attempt.
Vmo is a speed defined by the flight envelope which is based on Load Factor and Gust Factor and the effects of airspeed on the aircraft and control surfaces (for example flutter, and the region of reverse command). The top and bottom portions of the flight envelope have limits based on load factor and gust factors. The far right edge of the envelope is based on an airspeed at which adverse handling characteristics such as buffeting, flutter and reverse command on control surfaces could be catastrophic.
I did some computations and think I have a better understanding. For example, Vmo for the Beech 1900D is 248 knots from Sea Level to 13,200 feet. It then decreases from 248 knots to 195 knots (.48 Mach) from 13,200 ft to 25,000 ft. Below are some hypothetical scenarios. For example in the summer at sea level in Alaska on a standard day at 15 degrees and the winter it could be -30 C at the surface. While in a desert area it might be +38C. Some numbers might be a knot or two off as I used an actual E6B for True Airspeed Calculations and I don't have a calibrated airspeed.
But I think the results are close enough to help me understand the principle.
Conditions: Sea Level, +15C, 29.92, IAS 248 kts
Mach 1= (Square Root of 15C +273) multiplied by 39 = 661.8 knots
Mach .48 = 317 knots
TAS = 248 knots
So IAS and True Airspeed are equal and less than Mach .48
Conditions: Sea Level, +38C, 29.92, IAS 248 kts
Mach 1= (Square Root of 15C +273) multiplied by 39 = 687.7 knots
Mach .48 = 330 knots
TAS = 259 knots
So IAS is less than True Airspeed and both are less than Mach .48
Conditions: Sea Level -30C, 29.92, IAS 248 kts
Mach 1= Square Root of (-30C +273) multiplied by 39 = 607.9 knots
Mach .48 = 291 knots
TAS = 228 knots
So IAS is less than True Airspeed and both are less than Mach .48
Conditions: 13,200 ft, -11C, 29.92, IAS 248
Mach 1 = Square Root of (-11C +273) multiplied by 39 = 631.2 kts
Mach .48 = 303 knots
TAS = 304 Knots
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal
Conditions: 25,000 ft, -35C, 29.92, IAS 195 kts
Mach 1= Square Root of (-40C +273) multiplied by 39 = 595.3 knots
Mach .48 = 285 knots
TAS = 291 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal
Conditions: 25,000 ft, -20C, 29.92, IAS 195 kts
Mach 1= Square Root of (-20C +273) multiplied by 39 = 620.3 knots
Mach .48 = 297 knots
TAS = 300 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal
Conditions: 25,000 ft, -55C, 29.92, IAS 195 kts
Mach 1= Square Root of (-55C +273) multiplied by 39 = 575.8 knots
Mach .48 = 276 knots
TAS = 280 kts
So IAS is less than True Airspeed
Mach .48 and True Airspeed are approximately equal
In conclusion, Mach Speed is related to temperature. IAS decreases with an increase in altitude. At Sea Level the aircrafts TAS is well below the Mach .48 limit but still has a limit of 248kts IAS. The true airspeed is getting faster as we gain altitude for a given IAS of 248 kts. As we increase altitude, the margin between aircraft's TAS and Mach .48 get closer together. At a certain altitude these airspeeds meet and Mach.48 becomes the limiting airspeed.
