The natural frequency of wooden bats is around 250 cycles per second, or 250 Hertz. Because the ball leaves the bat so soon (1 millisecond), the energy transfer to the ball is not too efficient. If the bat has been hollowed and corked, it's no longer as stiff and it will get an even lower natural frequency and an even less efficient transfer of energy to the bat. The baseball bounces off the bat faster than the cork can store the energy that could be put back in the ball. The cork might deaden the sound of a hollowed out bat, but it doesn't propel the ball. It can't. So, balls hit with corked bats don't go as far.

Some Remarks on Corked Bats 
Alan M. Nathan

What is a “corked” bat?

A corked bat is one in which a cavity has been drilled axially into the barrel of a wood bat. Typically, the diameter of the cavity is approximately 1 inch and it is drilled to a depth of about 10 inches. The cavity may or may not be filled with some substance, such as compressed cork, small superballs, etc.

What positive effect does this have on performance?

Because wood has been removed from the bat and (possibly) replaced by some substance with a smaller density than wood, the bat is lighter by 1-2 oz., depending on the dimensions of the cavity and the density of the filling substance. Not only is the bat lighter, but the center of gravity, or balance point, of the bat moves closer to the hands. This means that the “swing weight” of the bat is also reduced. In technical physics language, the moment of inertia (MOI) of the bat about the knob is reduced for a corked bat. You can think of the MOI as the "rotational inertia" of the bat. Just like the "inertia" or mass of an object measures the resistance of the object to a change in its translational motion, the rotational inertia measures the resistance to a change in its rotational motion. The effect is easy to understand: It is much easier to swing something when the weight is concentrated closer to your hands (smaller MOI) than when it is concentrated far from your hands (larger MOI). You can try such an experiment yourself. Simply take a bat by the handle and swing try to rotate it rapidly. Then turn the bat around, holding the barrel, and try doing the same thing. You should find that it is easier to rotate it in the second case. Therefore, a batter can often get a higher bat speed with a corked bat than with a comparable bat that has not been corked. All other things being equal, a higher swing speed gives rise to a higher hit ball speed and greater distance on a long fly ball. Of course, all other things are not equal, and the reduced mass in the barrel produces a less effective collision, as we shall see in the next section.

An additional effect is that the lighter weight and smaller swing weight also lead to better bat control, which has a beneficial effect for a contact-type hitter, who is just trying to meet the ball squarely rather than get the highest batted ball speed. The batter can accelerate the bat to high speed more quickly with a corked bat, allowing the batter to react to the pitch more quickly, wait longer before committing on the swing, and more easily change in mid-swing. As has been pointed out by Bob Adair in his book, a batter can achieve the same effect legally by choking up on the bat or by using a lighter (and therefore probably shorter) bat. Of course, there are reasons one might not want to either choke up or use a shorter bat, especially in situations where you need to protect the outside part of the plate. In such a situation, a corked bat can provide a definite advantage. Many fast-pitch softball players take the issue of bat control to the extreme. This is why regulation softball bats are so important. The fast-pitch game heavily favors the pitcher, so a batter is often more interested in making good contact than in swinging for the fences. These batters use very light bats—25 oz. or less-- to improve bat control and reaction time. Since they are using primarily aluminum bats, they can achieve low weight with no cost in length.