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Could someone please help me understand a small but significant step in the derivation of the wave equation for a string with stiffness.

I am trying to follow the notes here:

http://courses.physics.illinois.edu/phys406/Lecture_Notes/Waves/PDF_FIles/Waves_2.pdf

The statement I don't understand is near the bottom of page 2 where ∂ϕ(x,t)/∂x ≅ −(∂2y(x,t)/∂x2)

I know sin(phi) ~ tan(phi) ~ opp/adj but this doesn't seem to help.

Any help greatly appreciated. :-)

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# Small Angle Approximation with a Stiff String

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