  We have measured the speed of both pressure waves and shear waves as a
function of depth between 80 and 500 m depth in South Pole ice with better than
1% precision. The measurements were made using the South Pole Acoustic Test
Setup ({SPATS}), an array of transmitters and sensors deployed in the ice at
South Pole Station in order to measure the acoustic properties relevant to
acoustic detection of astrophysical neutrinos. The transmitters and sensors use
piezoceramics operating at $\sim$5-25 kHz. Between 200 m and 500 m depth, the
measured profile is consistent with zero variation of the sound speed with
depth, resulting in zero refraction, for both pressure and shear waves. We also
performed a complementary study featuring an explosive signal propagating from
50 to 2250 m depth, from which we determined a value for the pressure wave
speed consistent with that determined with the sensors operating at shallower
depths and higher frequencies. These results have encouraging implications for
neutrino astronomy: The negligible refraction of acoustic waves deeper than 200
m indicates that good neutrino direction and energy reconstruction, as well as
separation from background events, could be achieved.
