String stiffness makes higher frequencies travel faster, changing 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

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

Categorization

• XREF: Explains why piano and guitar string timbre varies with thickness — connects to psychoacoustic perception of tone color. — connects to: The inharmonicity of real strings is a desirable feature, not a defect; 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 (+7 more)
• SEED: A concrete mechanism for why instruments in the same family sound different — supports writing on timbre and tone color.
• DEFINE: Explains why the ideal-string equation breaks down in real strings and names stiffness as the culprit.
• corroborated: 5 independent passages support this claim — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 103

Broader Connections

• String stiffness raises component mode frequencies above the harmonic series, creating inharmonicity #expands (0.90)
• Octave stretching on pianos emerges directly from string inharmonicity #expands (0.85) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 1096