{-# LANGUAGE TypeOperators #-}

import Data.Metrology
import Data.Metrology.Show
import Data.Metrology.SI
import Data.Units.US
د² = sTwo
د³ = sThree
g = 9.81 % Metre:/Second:^د² :: Acceleration

stringTension :: Length -> Mass%/Length -> Frequency -> Force
stringTension l ρ ν = ρ |*| (2 *| l |*| ν)|^د²

stringTension (327 % Milli:@Metre) (0.7 % Gram:/Metre) (440 % Hertz) -- Violin a-string

stringTension (0.7 % Metre) (5.7 % Gram:/Metre) (98 % Hertz) -- Cello G string

stringTension (25.5 % Inch) (0.00032 % Pound:/Inch) (110 % Hertz)  -- Electric guitar A string

type Gauge = Length -- thickness, i.e. diameter
steelstring :: Gauge -> Mass%/Length
steelstring d = (7.859 % Gram:/(Centi:@Metre):^د³ :: Density) |*| (pi *| (0.5*|d)|^د²)
                -- http://www.wolframalpha.com/input/?i=steel+density 

stringTension (25.5 % Inch) (steelstring $ 0.010 % Inch) (330 % Hertz)  -- Electric guitar e string

it |/|g#Pound   -- same string, tension in pound-force