Find the solution to Problem in terms of traveling waves.ProblemIn section 3.9, we showed...

Find the solution to Problem in terms of traveling waves.

Problem

In section 3.9, we showed how Fourier series could be used to represent a periodic function. Here we wish to apply that analysis to a vibrating string. Assume that a string of length l of mass per unit length μ. is stretched horizontally between two supports and held with tension F0. Assume that the middle of the string is displaced a distance a (where a «l) in the vertical direction. When the string is released, it vibrates in a standing wave pat­tern. Use Fourier analysis to calculate the pattern of vibration as a function of time (Figure P 11.29), that is calculate the Fourier coefficients of the series needed to describe the motion.

Figure