Editing Dispersion relation (section)

===Waves on a string===
{{Further|Vibrating string}}
[[Image:Two-frequency beats of a non-dispersive transverse wave (animated).gif|frame|right|Two-frequency beats of a non-dispersive transverse wave. Since the wave is non-dispersive, {{colorbull|red|circle}} phase and {{colorbull|limegreen|circle}} group velocities are equal.]]

For an ideal string, the dispersion relation can be written as

: <math>\omega = k \sqrt{\frac{T}{\mu}},</math>

where ''T'' is the tension force in the string, and ''μ'' is the string's mass per unit length. As for the case of electromagnetic waves in vacuum, ideal strings are thus a non-dispersive medium, i.e. the phase and group velocities are equal and independent (to first order) of vibration frequency.

For a nonideal string, where stiffness is taken into account, the dispersion relation is written as

: <math>\omega^2 = \frac{T}{\mu} k^2 + \alpha k^4,</math>

where <math>\alpha</math> is a constant that depends on the string.