Anomalous ultrasound propagation in the high-$T_c$ superconductors: ${\mathrm{La}}_{1.8}$${\mathrm{Sr}}_{0.2}$${\mathrm{CuO}}_{4\mathrm{-}\mathrm{y}}$ and ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

Attenuation and velocity of longitudinal ultrasound in both known classes of the high-$T_c$ copper-oxide superconductors are found to be highly anomalous compared to conventional superconductors. Attenuation shows a pronounced peak below $T_c$ followed by an approximately power-law decrease at low T. The velocity shows a discontinuity in its temperature derivative at $T_c$ followed by a large increase. The results are inconsistent with dominant contributions from the carriers alone. Anomalies are also observed at higher temperatures suggesting the existence of other phase transitions.