Ultrasonic attenuation in a pseudogapped superconductor

We develop a theory of ultrasound decay rate $\alpha$ in a model of a superconductor with a large pseudogap $\Delta_P$, and show that at low temperatures ($T \ll T_c$) the magnitude of the decay rate $\alpha$ is controlled by the ratio of $T/\Delta$, where $\Delta \ll \Delta_P$ is a superconducting collective gap. Thus we propose new method to measure the collective gap $\Delta$ in a situation when strong pseudogap is present.