A longitudinal sinusoidal wave of frequency ω is running along a chain of balls of mass m each, connected by springs of length l and stiffness k = mω₀². The longitudinal displacements of the balls are plotted vertically in the figure in an enlarged scale. The amplitude of the displacements A is much smaller than l. Find the speed of propagation of this wave. Obtain the velocity of this wave in the low-frequency limit (ω≪ω₀) through l and k, and then through Young's modulus E and matter density ρ, treating the balls as analogs of matter atoms. Estimate ω₀ for iron.
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3.7 Wave propagation