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Alfvén Wave Speed from Field and Mass Density

Calculate alfvén wave speed from field and mass density with compatible units, known-value inputs and clearly stated model assumptions.

Formula & worked example
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Calculator inputs

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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

For the worked inputs, Velocity is approximately 28.209479 kmps.

velocity = B / √(μ₀ρ)

Worked example

Enter these known values and leave the other values blank.

Magnetic field: 1 µT
Plasma mass density ρ (kg/m³): 1 × 10⁻¹⁵ kg/m³

Velocity: 28.21 km/s

Assumptions and limitations

Density means plasma mass per volume in kg/m³, not an ion count per volume.
The nonrelativistic ideal-MHD model is valid when its assumptions hold; it can predict unphysical speeds at very low density and is not a relativistic replacement.
The field and resulting wave speed are nonnegative magnitudes.
Numerical arithmetic uses 64 significant digits; displayed values are rounded separately. Captured particle-mass and astronomical unit conversions retain their stated approximations.

Common questions

Which inputs and assumptions does this result use?

Density means plasma mass per volume in kg/m³, not an ion count per volume.

References

Bookify retains the captured physical relationship and inverse controls, while replacing older or rounded constants with the 2022 CODATA values and full-precision π where applicable. Measured constants retain their physical uncertainty. Bookify requires physically valid mass or nonnegative field/speed magnitudes and principal scattering angles for this stated model.

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