Looking at the mouthpiece of a trumpet, you can easily see that there is nothing inside it to vibrate. It is a cold peice of metal and without a skilled player, it can do nothing. All of the vibrations that have to occur to produce a sound come from the player's lips vibrating at a high speed (this is referred to as buzzing the mouthpiece). The mouthpiece simply gives the lips a place to vibrate, and harnesses the vibrations. Many people think that brass instruments work like old-time phonograph players, that had a bell-like funnel that would simply amplify the sounds made by the stylus on the record. This is not true on brass instruments, however. The bell is not attached to the mouthpiece to amplify it, but to harness the sound wave produced by your "buzzing." The wave travels down the length of tubing, and when it reaches the end of he bell, it travels back to the mouthpeice and forms a "node" in the flared end of the bell. This produces what is known in physics as a standing wave, and can be explained scientifically.
When a player begins to buzz the mouthpeice, he or she produces a sound wave that travels the length of the tubing. As the wave reaches the end of the tubing, it encounters a sharp drop in impedance (resistance) which causes the wave to change direction and reflect itself back into the bell. When it reaches the mouthpeice, it is modified by the lips to produce a certain frequency. The lips are changed by the reflected wave so that they then correspond to the trumpet's pitch and tone color. In this process of waves bouncing back and forth, the standing wave is created. The entire process takes place in only a fraction of a second. In this whole process, however, a little acoustic (sound) energy is lost to the enviroment.
As the player plays higher, the point in the bell where the sound wave is reflected moves toward the bell, which means that more and more energy is lost, and less is reflected back to the mouthpeice. This is why it is increasingly difficult to play very high notes. Once the trumpet has reached E above the treble staff, there is very little energy if any that is reflected, and the trumpet then simply becomes a megaphone for the lips.