  Ultrasound wave propagation in a nonhomogeneous linearly elastic layer of
constant thickness is considered. The resonances for the corresponding acoustic
propagator are studied. It is shown that the distribution of the resonances
depends on the smoothness of the coefficients. Namely, if the coefficients have
jump discontinuities at the boundaries, then the resonances are asymptotically
distributed along a straight line parallel to the real axis on the unphysical
sheet of the complex frequency plane. In the contrary, if the coefficients are
continuous, then it is shown that the resonances are asymptotically distributed
along a logarithmic curve.
  The spacing between two successive resonances turns out to be sensitive to
articular cartilage degeneration. The application of the obtained results to
ultrasound testing of articular cartilage is discussed.
