Ultrasound velocity measurements based on a phase comparison method for fou
r different modes have been done on a copper-free layered perovskite superc
onductor Sr2RuO4 With T-c = 1.2 K. Anomalous softening is observed in the l
ongitudinal C-11 and C-33 modes below 108 K, which is attributed to the cou
pling of the electronic states to the strain with Gamma(1) representation i
n the tetragonal point group D-4h The discontinuous change of the slope in
C-11 and C-33 at Te is basically explained by the second-order strain depen
dence of T-c, partial derivative(2)T(c)/partial derivative epsilon(uk)(2).
From the initial slope of the upper critical field H-c2, the anisotropy rat
io in the coherence length is found to he 28, in agreement with previous ac
susceptibility measurements. Acoustic de Haas-van Alphen oscillations for
the cylindrical alpha-Fermi surface with 3.2m(0) are observed in C-33 as a
function of the magnetic field applied perpendicular to the Q2D conducting
plane. The area coefficient is evaluated to be \Lambda(zz)\ = 20+/-5 from t
he Kataoka-Goto model. The multiband term \Lambda(zz)(m)\ contributes domin
antly to \Lambda(zz)\, which corresponds to the interband charge transfer.