Stiffness makes transversal waves dispersive and their modal tones inharmonic

Evidence

An example of transversal waves that resemble string behaviour but which are not purely one-dimensional and harmonic in spectral content is wave propagation in a bar. Due to bending stiffness, the transversal waves are dispersive, implying that different frequencies propagate at different velocities (higher frequencies propagate faster than lower ones). This results in modal frequencies that do not have a harmonic relationship. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 248

Categorization

• XREF: Explains why percussion and struck-bar instruments like marimbas and church bells sound inharmonic — connects to the science of instrument design and why metal bars are tuned by carving. — connects to: String and pipe resonance differ in transverse versus longitudinal wave motion — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1132