Bending waves disperse with frequency, so their waveshape is not preserved

Evidence

Equation 1.11 is significantly different from that for quasi-longitudinal and transverse shear waves. In particular, the velocity is now frequency dependent and increases with frequency. This results in dispersive propagation of waves with different frequencies traveling at different velocities. Therefore waveshape is not preserved in bending wave propagation. One can hear the effect of this if one listens to the “chirp” sound emitted by ice covering a pond when hit by a thrown rock. The dispersion and the fourth root arise because, unlike quasi-longitudinal and transverse shear waves, the spatial derivatives in the wave equation are fourth order instead of second order because the bending wave is an amalgam of longitudinal and transverse waves. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 128

Categorization

• CANDY: The ice-on-a-pond chirp is a delightful everyday example of dispersion that would make a great elevator-conversation tidbit about sound.
• SHARE: Good for anyone who loves skating or pond ice sounds — explaining why the thrown-rock chirp descends as the wave disperses.
• corroborated: 5 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 128
• XREF: connects to: Bending wave speed grows as the square root of frequency; A bowed string vibrates as a traveling kink, not as smooth standing waves; Dispersive waves in stiff bars produce inharmonic modal frequencies (+2 more)

Broader Connections

• Longitudinal and shear waves preserve waveshape because phase velocity is frequency-independent #corroborates (0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 132