why faster aircraft use turbofans compared to slower aircraft using turboprops
The short answer is that, in the domain of most subsonic business and commercial aircraft, there is actually no aerodynamic constraint preventing turboprops from competing in speed and efficiency with turbofans.
A longer answer might benefit from some books or courses, but I'll take a stab at an executive summary, as this is an area I've spent some time researching.
The introductory thing you need to understand is that some of the terminology results solely from historical marketing pressures. The term ''propfan'' was coined to get away from the old-fashioned association of a propeller. A propfan is, in every way, a propeller. The "fan" inside a turbofan is also a propeller. Of course, in each instance, for any airplane, the design of the propeller must be optimized for its range of freestream conditions.
Once you understand this, you can appreciate that the major distinctions with a difference wrt turbine propulsion involve: (i) ducted vs unducted propeller, (ii) bypass ratio, (iii) overall propulsive efficiency.
The first key thing to understand about propellers is that a propeller blade is a wing (and actually wings can be viewed as a propeller disc of equivalent span). Just as what keeps an airplane aloft in straight-level flight is the downward thrust vector from the airflow as it is slightly redirected downward by the wing (think Newton's 3rd law), the propeller blade redirects some of the local airflow across the blade into the axial direction, thus adding thrust.
The second thing to understand is that in subsonic aerodynamics, "jet" is actually a four-letter word. You see, a jet, by definition, is a relatively fast-moving focused stream of fluid, and this is also a definition of inefficient propulsion. To maximize subsonic propulsive efficiency, you want to move a large area of air at a speed that is just
slightly higher than the freestream velocity (i.e., the exact opposite of a jet). Incidentally, this is why helicopters have very large diameter blades, so they can maximize the propulsive efficiency at very low speed. And recalling the first point that wings and propellers work the same, this is also the reason why sailplanes have long wings, so that the downward airflow resulting from the wings (aka "lift") is spread over a large area and is thus slow-moving -- and thereby efficient.
A third thing to understand, just to complicate matters, is that the jet engine is a truly bizarre engine in that it has constant thrust instead of constant power (for a given fuel flow across varying freestream velocities). Strange realizations ensue from this bizarre bit of thermodynamics. For example, the faster a jet engine goes, the more efficient it becomes (and the slower it goes, the less efficient) in terms of power per fuel flow. So if you're going to design a jet, it should go fast.
But even when flying fast and subsonic, the inefficient propulsion of the jet exhaust stream begs for some improvement, and this is where the turbofan comes in (and why there hasn't been a
true commercial or business jet airplane in 40 years).
Back to nomenclature, a ducted propeller coupled with a jet engine is called a turbofan; however, the bypass ratio -- the ratio of mass flows between propeller and jet engine -- can vary considerably. You can loosely think of the bypass ratio as the ratio between high efficiency propeller thrust (slow moving, large area) and low efficiency jet thrust (fast moving, small area).
So why don't all turbofans have very high bypass ratios? It is for a number of reasons. The size, drag, and weight of the fan and shroud can become considerable at high bypass ratios. Other engineering constraints, such as the optimal vs constrained fan rpm (if an ungeared fan) must also be considered, as must other things such as high altitude considerations.
Now we need to dispel a prevalent myth about propellers. It is absolutely
not true that propellers must lose much of their efficiency at supersonic speeds. Actually, if properly designed, propellers can operate with very high efficiency, almost as high as conventional low speed propellers, far in the supersonic regime. The main constraint has much more to do with noise and vibration than efficiency. And note that the ducted propeller of a modern commercial aircraft turbofan is often designed to reach around Mach 1.11 local tip velocity for takeoff.
So could a business or commercial aircraft be designed for Mach 0.80 flight with an unducted propeller (aka propfan)? YES. In fact, it has been demonstrated with many different tests. Would it have greater propulsive efficiency than a turbofan? YES (but moreso at Mach 0.76 than Mach 0.90 because of the jet engine speed-efficiency relationship described above). But the current downsides are noise, vibration, and perception. Where the industry appears to be going, at present, is towards even larger turbofans with higher bypass ratios, geared fans, and variable pitch blades.
Unbeknownst to much of the public, the propeller actually made a huge comeback in the 1970's after being displaced by the sexy jet with its concealed thrust mechanism, but the propeller had to sneak back onto the stage, hidden inside the duct of every turbofan. In the future, the propeller may again wholly emerge from its cloak as an "unducted rotor," "propfan," or some clever name yet to be trademarked. And in the very long term, calculations show the unducted propeller should ultimately win out for subsonic transportation, at least up to about Mach 0.80-0.85.