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This is basically the wave equation with Δm representing a small piece of mass from an interval of the string and two forces added to the right side.

He defines the drag from air friction as F = -C*A*v^2. I can accept this. However, he then defines area with A = 2 * σ * Δx. I'm not sure of what σ means here.

Δx would be expected to represent the length of the string fragment corresponding to Δm. But what is σ? How does this give you area of the string? I know volume of string segment would be V = π * r^2 * Δx. Cross sectional area would be A = π * r^2. If you tried to imagine it as a flat object like a billboard you could say A = 2 * r * Δx. So is that what he's doing? Is σ radius?

I've never seen it used that way and searching "σ radius" gives no results suggesting it's commonplace. He doesn't define sigma anywhere in the article, so I presume you're just supposed to know.

Is this likely the correct interpretation and is this normal notation for radius?

Thanks