Question on waves propagation from a moving frame

[QuArK21343]

In my book on waves, it is said that, given a flexible string under tension, a derivation of the transverse velocity v can be given by viewing the string in a frame moving uniformly with a velocity equal to that of the wave itself. The velocity can be found by requiring the uniform tension of the string give rise to a centripetal force on an element $\Delta s$ of the string so to produce a circular motion. I seem to be lacking the physical intuition behind this situation. I don't quite understand how the centripetal motion arises: aren't the oscillations supposed to be transversal?

 

[danmay]

In my book on waves, it is said that, given a flexible string under tension, a derivation of the transverse velocity v can be given by viewing the string in a frame moving uniformly with a velocity equal to that of the wave itself. The velocity can be found by requiring the uniform tension of the string give rise to a centripetal force on an element $\Delta s$ of the string so to produce a circular motion. I seem to be lacking the physical intuition behind this situation. I don't quite understand how the centripetal motion arises: aren't the oscillations supposed to be transversal?

Maybe it meant in the complex plane. One sinusoidal oscillation along the real number axis plus another sinusoidal oscillation along a perpendicular imaginary number axis would form uniform circular motion in the combined complex plane (real numbers being a subset of complex numbers).