According to the pokédex, Pidgeot can fly as fast as Mach 2. But how fast is that for a bird?
Lets start off by discussing what Mach speed is. Mach is essentially the measurement which is based on the speed of sound. Mach 1 would be the speed of sound. Mach 2 would be twice the speed of sound, and so on.
There are different regimes or “classifications” of Mach speed. They range from Subsonic speeds below 0.8 Mach, to re-entry speeds larger than 25.0 Mach. In Pidgeot’s case, it is said to travel at a speed of Mach 2, thus putting it in the supersonic speed regime. The scientific formula for Mach number is:
M is the Mach number
u is the local flow velocity with respect to the boundaries
c is the speed of sound in the medium
Essentially the Mach number depends on the conditions surrounding medium. Sound travels faster through water than it does through air. Therefore, something swimming at Mach 2 through water would actually be moving faster than a bird going Mach 2 in air. Mach is measured relatively in that way. For the case of Pidgeot, the medium would be air: and the Mach speed would depend in particular on the temperature and pressure. Sound travels at 1,225 km/h at sea level. A Pidgeot at Mach 2 would be going at 2,450 km/h.
Now how does all this relate to birds and speed of flight? The fastest known bird in our universe is the Peregrine falcon. This bird can travel at a maximum air speed of 389 km/h (242 mph) and an average diving speed of 180 km/h (112 mph).
That being said, a Pidgeot traveling at Mach 2 speed is traveling at 2450.088 km/h (1 522.4141 mph). That is way faster than the Peregrine falcon could ever fly.
In fact, the first recorded speed of Mach 2 was by a Douglas D-558-2 Skyrocket on November 20, 1953. No bird has ever reached any speed remotely close to these speeds.
So Pidgeot travelling at Mach 2 speeds? It is a possibility, but it would have to be one hell of a bird to survive.