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When pressure is the only restoring force (i.e., g=0), Eqn. 41 becomes,

(42) 
and assuming a compressible gas (i.e., ), this simplifies by taking the square root of the dot product with k to,

(43) 
the dispersion relation for acoustic waves. Hence acoustic waves are longitudinal (v_{1} is along k), nondispersive (phase velocity v_{p} = ω/k = c_{s} and group velocity v_{g} = dω/dk = c_{s}are equal), and isotropic (phase speed does not vary with k).
James McAteer
20040114