The pulse broadening and decay of coherent sound waves propagating in disordered granular media are investigated. We find that the pulse width of these compressional waves is broadened when the disorder is increased by mixing the beads made of different materials. To identify the responsible mechanism for the pulse broadening, we also perform the acoustic attenuation measurement by spectral analysis and the numerical simulation of pulsed sound wave propagation along one-dimensional disordered elastic chains. The qualitative agreement between experiment and simulation reveals a dominant mechanism by scattering attenuation at the high-frequency range, which is consistent with theoretical models of sound wave scattering in strongly random media via a correlation length.