  Measurement of the differential rotation of the Sun's interior is one of the
great achievements of helioseismology, providing important constraints for
stellar physics. The technique relies on observing and analyzing
rotationally-induced splittings of p-modes in the star. Here we demonstrate the
first use of the technique in a laboratory setting. We apply it in a spherical
cavity with a spinning central core (spherical-Couette flow) to determine the
mean azimuthal velocity of the air filling the cavity. We excite a number of
acoustic resonances (analogous to p-modes in the Sun) using a speaker and
record the response with an array of small microphones on the outer sphere.
Many observed acoustic modes show rotationally-induced splittings, which allow
us to perform an inversion to determine the air's azimuthal velocity as a
function of both radius and latitude. We validate the method by comparing the
velocity field obtained through inversion against the velocity profile measured
with a calibrated hot film anemometer. This 'modal acoustic velocimetry'
technique has great potential for laboratory setups involving rotating fluids
in axisymmetric cavities. It will be useful especially in liquid metals where
direct optical methods are unsuitable and ultrasonic techniques very
challenging at best.
