Waves in an Impossible Sea by Matt Strassler

Author:Matt Strassler [STRASSLER, MATT]
Language: eng
Format: epub
Publisher: Basic Books
Published: 2024-03-05T00:00:00+00:00

Figure 34: A simple sound wave traveling to the right (long gray arrow). It has crests (more concentrated air, in darker shading and indicated with vertical arrows) and troughs (less concentrated air, in lighter shading). The wind field is rippling, too (black arrows).

Meanwhile, the wind is also rippling. For air to become more concentrated somewhere, it must flow into that location. Similarly, the air must flow out of places where it is becoming less concentrated. In short, wind blows into crests and out of troughs. These flows are indicated by the black horizontal arrows in the figure. At the center of a trough or crest, the wind field drops to zero.

So in this snapshot, the wind has its own ripples—rightward, then zero, then leftward, then zero, then rightward again—over and over across the sound wave. This whole rippling pattern of the wind field moves to the right in lockstep with the rippling pattern in the air. So if we take a field-centric perspective, focusing on the wind instead of the air, we could describe this sound wave as ultimately a wave in the wind field—a wave in a property of the medium called air.

There’s only one wave here, not two. A ripple in the air can’t exist without a ripple in the wind, and vice versa; that’s what Fig. 34 illustrates. So our two perspectives are simply two ways of looking at a single wave: one emphasizes the air, the other emphasizes the wind. Which one we choose is up to us. For those of us who know about air, wind, and sound—medium, field, and wave—both perspectives are equally good, even though the latter may seem a little odd and unusual at first.

But now imagine that you have only part of this picture. You’re a scientist who knows nothing about the existence of air or of the rippling pattern illustrated by the shaded regions in Fig. 34. All you can measure are the black horizontal arrows; all you can know is that the wind is rippling and that its ripple is traveling to the right.

This is the challenge for those poor scientists: they can measure the wind, but they don’t know more fundamentally what it is that they are measuring. Nevertheless, using experiments and observations, they can learn what the wind field does: it knocks trees down when it’s strong; it can spiral around in tornadoes; it can push on walls and eardrums. They can write detailed formulas for its behavior. They can learn a great deal about sound waves, too: amplitude, frequency, speed, and effects on human ears. They can observe that when you and I hear sound, there’s always a wave in the wind field that’s responsible. And so they will naturally adopt the field-centric perspective and describe sound as a traveling wave in the wind.

In a sense, this perspective is incomplete. Conceptualizing sound waves purely in terms of wind leaves out their fundamental relationship with air. But until the scientists know what’s missing from their knowledge of sound and wind, it will have to do.

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