   Next: Fourier Analysis of (4.15) Up: Magnetohydrodynamic Waves Previous: Linearised MHD Equations

# Sound Waves - Basic Waves Properties

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 non-zero. This means that sound waves are compressional.

Subsections   Next: Fourier Analysis of (4.15) Up: Magnetohydrodynamic Waves Previous: Linearised MHD Equations
Prof. Alan Hood
2000-01-11