Real string stiffness slightly raises wave velocity with frequency, affecting timbre.

Evidence

This equation, although it is derived assuming an infinitely thin string, is applicable to most strings that one is likely to meet in practice. But it is applicable to only pure transverse vibration; it does not apply to other modes of vibration. However, transverse waves are the dominant form of vibration for thin strings. The main error in Equation 1.7 is due to the inherent stiffness in real materials, which results in a slight increase in velocity with frequency. This effect does alter the timbre of percussive stringed instruments, like the piano or guitar, and gets stronger for thicker pieces of wire. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103 (#exemplifies, via linked claim)

Categorization

• XREF: connects to: A string’s stiffness raises its higher-frequency modes above the ideal values — Eric J. Heller, Why You Hear What You Hear- An…, 860; Violin timbre changes with direction as high frequencies become increasingly directional — Eric J. Heller, Why You Hear What You Hear- An…, 1785; String stiffness makes higher frequencies travel faster, changing timbre — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103 (+4 more)

Broader Connections

• String stiffness makes higher frequencies travel faster, changing timbre #exemplifies (0.95) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103
• Instrument stiffness versus tension determines how widely its modes are spaced #corroborates (0.75)
• Denser materials slow sound while stiffer bonds speed it up #expands (0.75)
• String stiffness raises component mode frequencies above the harmonic series, creating inharmonicity #contradicts (0.70)
• Shear waves resist deformation via stiffness rather than tension #expands (0.70)