Bending waves disperse because their wavenumber grows only with the square root of frequency

Evidence

The first is that the wavenumber of lateral shear waves is proportional to frequency, just as one would expect from a nondispersive wave. However, for a bending wave, the wavenumber rises only as the square root of frequency. In both cases, the coefficient is inversely proportional to the phase velocity, so a low slope implies a high phase velocity. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 157

The first is that the wavenumber of lateral shear waves is proportional to frequency, just as one would expect from a nondispersive wave. However, for a bending wave, the wavenumber rises only as the square root of frequency. In both cases, the coefficient is inversely proportional to the phase velocity, so a low slope implies a high phase velocity. It is often helpful to plot wavenumber versus angular frequency in a dispersion diagram. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 157

Categorization

• DEFINE: Clarifies dispersion in terms of wavenumber-frequency relations for shear versus bending waves, distinguishing them from nondispersive waves.
• corroborated: 3 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 157