An incident sinusoidal wave on a string (amplitude A, wave number k, wavelength A, angular frequency W, wave speed v) tr

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An incident sinusoidal wave on a string (amplitude A, wave
number k, wavelength A, angular frequency W, wave speed v) travels
in the negative x direction. At a fixed end, the wave is
reflected. a) Write the wave function of the incident wave y and of
the reflected wave y as a function of x and t. b) Use the principle
of superposition and derive an equation for the resulting standing
waves. c) Give the position of the nodes as a function of 1. d) We
now assume that the positions x=0 and x=L are fixed end. Show that
the standing waves exist for frequencies fn=nv/(2L