String pitch rises with tension and falls with length and density

Evidence

Equation 8.8 captures the Mersenne laws of vibrating strings: their frequency is inversely proportional to the length of the string, proportional to the square root of the tension, and inversely proportional to the square root of the density of the string per unit length. — Eric J. Heller, Why You Hear What You Hear- An…, 817

Categorization

• DEFINE: States the Mersenne laws governing string frequency in terms of length, tension, and linear density.
• XREF: These laws explain why plucked or bowed instruments (guitar fret placement, tuning pegs, gut vs. steel strings) behave as they do — connects directly to the reader’s living-root-bridge and crafting material. — connects to: When a string’s linear density is fixed, pitch is varied by tension and length — David Howard, Jamie Angus, coustics and Psychoacoustics, 1093
• SHARE: Would be a fun physics nugget for anyone who tunes or builds stringed instruments.