When a transverse sinusoidal wave is present on a string, the particles of the string undergo SHM. This is the same motion as that of a mass m attached to an ideal spring of force constant k', for which the ~ frequency of oscillation was found in Chapter 13 to be w = √k'/m. Consider a string with tension F and mass per unit length IL, along which is propagating a sinusoidal wave with amplitude A and wavelength A.
(a) Find the ''force constant" k' of the restoring force that acts on a short segment of the string of length Δx (where Δx « A).
(b) How does the "force constant" calculated n part (b) depend on F, µ, A, and A? Explain the physical reasons this should be so.