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Consider the simplest wave problem first by setting the magnetic
field and gravity to zero. This is equivalent to a high
plasma and is valid for lengths that are much shorter than the
pressure scale height. Thus, the equilibrium satisfies
The equilibrium is uniform. No restriction is placed on
, the equilibrium density but, for simplicity, it is also
assumed uniform as well.

(4.12) 
With (4.12), (4.11) reduces to

(4.13) 
To progress, define
and take the
divergence of (4.11). This gives a simple wave equation for
the scalar quantity of the form
The characterstic speed is the sound speed, , where

(4.14) 
and the wave equation for sound waves is

(4.15) 
Notice that these waves travel at the speed of sound and assume that
is nonzero. This means that sound waves are compressional.
Subsections
Next: Fourier Analysis of (4.15)
Up: Magnetohydrodynamic Waves
Previous: Linearised MHD Equations
Prof. Alan Hood
20000111