July 3, 1961

Dear Mr. McQuigg

I figured out the effect of wire stiffness on the vibration frequency of strings. The mathematical formula is [note 1]

t r u e f r e q u e n c y = f ( 1 + π 2 E A 2 µ T 2 f 2 ) ,

where f is the frequency you would get forgetting about stiffness (for fundamental

f = 2 l T µ

[note 2] for string of length l), T is the tension in the string, A is the area of the string cross-section, E is Young’s modulus of steel (measures the stiffness of the wire), µ is the weight of wire per unit length = 7.80 grams × A in squ. centimeters for steel. I have worked this out roughly for steel wires—not for the weighted bass strings. It says that the frequency...

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