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Unformatted text preview: Standing Waves Prelab 1 Guitar String 1.1 Linear Mass Density For a steel wire of diameter D = 0 . 010 inches and density = 7 . 80 g/cm 3 , what is the linear mass density of the string? The definition of volume mass density is mass per unit volume, = m V The mass m of the guitar string is therefore m = V In order to calculate the volume of the steel wire, we will model the wire as a cylinder of length L and diameter D , V = AL = ( r 2 ) L = D 2 2 L = D 2 L 4 We can now rewrite the expression for the mass of the wire, m = V = D 2 L 4 The definition of linear mass density is mass per unit length, = m L Using the expression for the mass, = m L = D 2 4 = D 2 4 The length of the wire cancels out: the linear mass density of a very long wire is equal to that of a short piece of wire. We can use the known values for and D in order to calculate , = D 2 4 = ( 7 . 80 g cm 3 ) (0 . 010 in ) 2 4 Remembering that 1 in = 2 . 54 cm ,...
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