The demonstration relies on the properties of sound and the phenomenon of resonance. Two bottles facing in opposite directions are attached to the ends of a stick, which is suspended over a loudspeaker. Remarkably, when a loud sound matching the natural frequency of the bottles is played, the bottles begin to rotate without the application of any other external force.
Download video of my demonstration
The majority of the demonstration can be explained by resonance. When I play a sound that matches the natural frequency of the bottles, the air in the bottles begins to vibrate at very large amplitudes. When I increase the volume of the sound while keeping the frequency constant, the air in the bottles vibrates at even larger amplitudes. Note that, though it is difficult to tell from the video, the sound played is very loud. Ear protection is essential. The demonstration will not work successfully at low volumes; the sound needs to be loud to create vibrational amplitudes that are large enough to set the system into motion. Similarly, as shown in the video, the system will not move at frequencies other than the natural frequency, which is needed to achieve resonance.
This, however, is only part of the picture. As discussed in the physics section, the air is moving both in and out of the bottle, which gives rise to a puzzling problem: if air is being expelled and sucked in, what gives the bottles the net thrust they need in order to spin? The answer lies in how the air enters and exits the bottles. When air enters the bottle, which has a defined shape, it enters in a "collimated" fashion. When it exits the bottles, it is entering an environment that has no defined shape or volume. The air, therefore, simply gushes out, which essentially gives the bottles a net thrust.
This can be illustrated by a simple concept. If I have a lighted candle and I blow inwards, I will not be able to extinguish the flame no matter how hard I try. This is because the air enters my mouth in a collimated, orderly fashion, which pulls only a little on the candle but is ultimately ineffective in putting it out. If I blow outwards, the air moves in all directions and immediately extinguishes the flame. For a more detailed discussion and illustrations, please refer to slides 22-24 from my PowerPoint under the section "Lesson Plan."