[UPSC CSE 2005] Waves (Q54, 20M)

(b) For a transverse sinusoidal wave of wavelength \lambda propagating along negative x direction through a string fixed at a point, show that the nodes are located at x = 0, \lambda/2, \lambda, 3\lambda/2, \dots while the kinetic energy / unit length at the antinodes is given by E = 2 \rho A^2 \omega^2 \cos^2 \omega t where \rho, A and \omega, are the mass density / unit length, amplitude of transverse displacement and angular frequency of the wave, respectively.