  The acoustic spectrum of a gas-filled resonating cavity can be used to
indirectly probe its internal velocity field. This unconventional velocimetry
method is particularly interesting for opaque fluid or rapidly rotating flows,
which cannot be imaged with standard methods. This requires to (i) identify a
large enough number of acoustic modes, (ii) accurately measure their
frequencies, and (iii) compare with theoretical synthetic spectra. Relying on a
dedicated experiment, an air-filled rotating spheroid of moderate ellipticity,
our study addresses these three challenges. To do so, we use a comprehensive
theoretical framework, together with finite-element calculations, and consider
symmetry arguments. We show that the effects of the Coriolis force can be
successfully retrieved through our acoustic measurements, providing the first
experimental measurements of the rotational splitting (or Ledoux) coefficients
for a large collection of modes. Our results pave the way for the modal
acoustic velocimetry to be a robust, versatile, and non-intrusive method for
mapping large-scale flows. Pages: 1-14
