You are walking down a quiet grocery store aisle when suddenly a voice says: "Thirsty? Buy me." You stop in front of the soda display, but no one is next to you, and shoppers a few feet away do not seem to hear a thing.

At that moment, you are standing in a cylinder of sound. Whereas a loudspeaker broadcasts sound in all directions, the way a lightbulb radiates light, a directional speaker shines a beam of waves akin to a spotlight. The beam consists of ultrasound waves, which humans cannot hear, but which can emit audible tones as they interact with air. By describing these interactions mathematically, engineers can coax a beam to exude voice, music or any other sound.

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