When a transverse sinusoidal wave is present on a string,

Chapter 15, Problem 57P

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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 angular frequency of oscillation was found in Chapter 14 to be . Consider a string with tension ?F and mass per unit length ???, along which is propagating a sinusoidal wave with amplitude ?A and wavelength ?. (a) Find the “force constant” k' of the restoring force that acts on a short segment of the string of length ??x (where ??x ? ???). (b) How does the “force constant” calculated in part (b) depend on ?F?, ???, ?A?, and ???? Explain the physical reasons this should be so.