  We present measurements of the diffusion coefficient of ultrasound in
strongly scattering three-dimensional (3D) disordered media using the dynamic
coherent backscattering (CBS) effect. Our experiments measure the CBS of
ultrasonic waves using a transducer array placed in the far-field of a 3D slab
sample of brazed aluminum beads surrounded by vacuum. We extend to 3D media the
general microscopic theory of CBS that was developed initially for acoustic
waves in 2D. This theory is valid in the strong scattering, but still diffuse,
regime that is realized in our sample, and is evaluated in the diffuse far
field limit encountered in our experiments. By comparing our theory with the
experimental data, we obtain an accurate measurement of the diffusion
coefficient of ultrasound in our sample. We find that the value of $D$ is quite
small, $0.74 \pm 0.03$ mm$^2/\mu$s, and comment on the implications of this
slow transport for the energy velocity.
