How well would sound travel on Mars? A bit of analysis.

Sep 18 04:57 UTC 1998

From: Jason Goodman <goodmanj@ASmit.edu>
Newsgroups: sci.space.tech
Subject: Re: Martain EVA Suits?
Date: Fri, 31 Jul 1998 17:45:42 +0000
Organization: Massachusetts Institute of Technolohgy
Lines: 39
Message-ID: <35C202C6.729DC972@ASmit.edu>

Frank Crary wrote:
> I don't think that is entirely correct. I'd expect sound to carry
> farther on Mars. If memory serves, the damping of a sound wave
> depends on the viscosity of the medium, and the viscosity decreases
> with atmospheric density. 

Thermal diffusivity is also an important player.  It turns out (see
the appendix of "Fluid Dynamics for Physicists", by T.E. Faber) that
the amplitude of a sound wave decays like
   exp(-alpha x/lambda)
where the attenuation coefficient alpha is
  alpha ~ (20-30) l/lambda
where l is the mean free path of the gas molecules.  This result is true
for both thermal diffusivity and shear viscosity (with different
constants in front).
  So the amplitude goes like
    exp(- B l x/(lambda^2))
Since l ~ 1/rho, neglecting the change in lambda due to the (somewhat smaller)
sound speed on Mars, we find that attenuation distance
  x0 = lambda^2/(B l) = C lambda^2 rho
is smaller when the density is smaller, in contraditiction to your
statement.

However, there are lots of other important things going on, including
a sort of "resonance absorbtion" effect involving the vibrational
degrees of freedom of the molecules.

Figure A.2 in Faber's book shows that this resonance effect
is very strong for a 500-Hz oscillation in a 7 mbar, 23 C CO2 atmosphere. 
(sorry, figures for colder temps are not shown.)  This resonance effect also
dominates absorbtion in an oxygen atmosphere (Earth's), though the text says 
it is almost 100 times smaller.

I agree with you that making a loud sound in the first place is hard, but
it appears that absorbtion of sound in Mars's atmosphere is also very
strong.  Mars will be a quiet place.