  There are five distinct collective modes in the recently discovered p-wave
superconductor Sr$_2$RuO$_4$; phase and amplitude modes of the order parameter,
clapping mode (real and imaginary), and spin wave. The first two modes also
exist in the ordinary s-wave superconductors, while the clapping mode with the
energy $\sqrt{2} \Delta(T)$ is unique to Sr$_2$RuO$_4$ and couples to the sound
wave. Here we report a theoretical study of the sound propagation in a two
dimensional p-wave superconductor. We identified the clapping mode and study
its effects on the longitudinal and transverse sound velocities in the
superconducting state. In contrast to the case of $^3$He, there is no resonance
absorption associated with the collective mode, since in metals $\omega/(v_F
|{\bf q}|) \ll 1$, where $v_F$ is the Fermi velocity, {\bf q} is the wave
vector, and $\omega$ is the frequency of the sound wave. However, the velocity
change in the collisionless limit gets modified by the contribution from the
coupling to the clapping mode. We compute this contribution and comment on the
visibility of the effect. In the diffusive limit, the contribution from the
collective mode turns out to be negligible. The behaviors of the sound velocity
change and the attenuation coefficient near $T_c$ in the diffusive limit are
calculated and compared with the existing experimental data wherever it is
possible. We also present the results for the attenuation coefficients in both
of the collisionless and diffusive limits at finite temperatures.
