This is a fantastic question!
There are some sounds recorded by a GoPro camera high in Earth's atmosphere in the video linked in the question How did the tangential thrusters for the 2014 LDSD test spin-up then spin-down so nicely? also shown below.
The sound starts at 120,000 feet (36.4 km) and then is heard at about 180,000 feet (54.5 km). Using NASA's U.S. Standard Atmosphere 1976 (in the vicinity of page 60-ish) these translate to about 0.5% and 0.05% of Earth's standard (i.e. sea level) atmosphere, which is already Mars's surface pressure (at a high altitude) and much lower than that, respectively.
The sounds is fainter, as can be expected, since fewer air molecules with the same excitation will transmit less power, and answers to What is the relation of sound propagation to air pressure? confirm it's roughly proportional.
As long as the mean free path is much shorter than the wavelength of sound, which it will be on the surface of Mars, there will not be much of a frequency dependent attenuation. So you can assume that the sounds will be 1% as loud as they would be on Earth, but sound very similar.
For scalar sound waves, 10 dB in amplitude is 10 dB in power, so this will be a roughly 20 dB reduction in level, but otherwise sound similar.
This contrasts with vector electromagnetic waves where 10 dB in amplitude is 20 dB in power.