In its simplest form the siren consists of two metal disks, each having the same number of regularly spaced concentric holes. The lower disk is mounted on the base of the siren, while the upper disk is mounted on a steel shaft just above it. As air is forced through the system, the upper disk begins to rotate. As it spins, the holes in the two disks briefly line up and then quickly close. Each time they do this, a brief puff of air is released. Each of these puffs acts like a single sound wave, and if enough of them are produced we perceive them as a continuous musical sound.
The number of holes in the disk determines the number of “waves” produced on each rotation. And the total number of waves (or puffs of air) per second determines the frequency of the sound produced. As long as air flows through the siren, increasing the speed at which the upper disk rotates will raise the pitch of the sound produced.
Source: Steven Turner; Curator, Physical Sciences, National Museum of American History, Smithsonian Institution.
Further information on the Science Teaching Collection and the Smithsonian National Museum of American History can be found here.