The amount of elastic potential energy (EPE) stored in a string is given by the following equation

Where Δl is the extension resulting from the tensioning of the string and the plucking action, l is the natural length of the string and Qs is the net elasticity or ‘relative strength’ of the wire

Where

Q = Young's modulus

d = diameter

To calculate the amount of energy stored in a harp string with its known parameters when under tension the natural length l of the string must be established first in order to calculate the elongation Δl.

Let

Δl_{1} = the elongation resulting from the initial string tension

Δl_{2} = the elongation resulting from the plucking action

Δl = ??Δl_{1}+Δl_{2} = total elongation

l = the natural length of the string

l_{1} = the vibrating length of the string under tension

From Hooke’s Law

Values for Q_{s} (Q and d), l_{1} and T are known for any given string, allowing Δl_{1} to be calculated and therefore l, which is equal to l_{1}-Δl_{1}

The elongation resulting from the plucking action Δl_{2} can be calculated thus

Where P_{p} is the plucking point and P_{d} is the plucking depth.

Submitted by Paul Dooley, 21 March, 2013. © 2004-2013 Paul Dooley

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