  We report on experimental investigations of longitudinal collective
oscillations in a highly elongated, harmonically trapped two-component Fermi
gas with resonantly tuned s-wave interactions ('unitary Fermi gas'). We focus
on higher-nodal axial modes, which in contrast to the elementary modes have
received little attention so far. We show how these modes can be efficiently
excited using a resonant local excitation scheme and sensitively analyzed by a
Fourier transformation of the detected time evolution of the axial density
profile. We study the temperature dependence of the mode frequencies across the
superfluid phase transition. The behavior is qualitatively different from the
elementary modes, where the mode frequencies are independent of the temperature
as long as the gas stays in the hydrodynamic regime. Our results are compared
to theoretical predictions based on Landau's two-fluid theory and available
experimental knowledge of the equation of state. The comparison shows excellent
agreement and thus both represents a sensitive test for the validity of the
theoretical approach and provides an independent test of the equation of state.
The present results obtained on modes of first-sound character represent
benchmarks for the observation of second-sound propagation and corresponding
oscillation modes.
