We want    f   =  261.6 Hz   =   261.6  cycles/s

  The wire has

        length  L     =   1.00    meter

        diameter d    =   0.001   meter

        density rho   =   7800    kg/meter^3


  The desired angular frequency is

                omega  =  2 pi f  =  1644  rad/s


  The mass density of the wire is

                mu     =  pi (d/2)^2 rho   =   0.00613   kg/meter


  The speed of the wave along the wire must be

                v      =  lambda * f  =  (2 m) * (261.6 cycles/s)

                       =   523.2 meter/s


  So we can determine the required tension T in the wire via

                T
               ---     =   v^2
               mu


                T      =   mu * v^2  =  (0.00613 kg/m) * (523.2 m/s)

                       =   1678 N

                       =    378 lb 


  That's a lot of force, and this is just one wire, out of (at least)
88 for a full piano.  There is a reason that "plate" which holds
the strings in a piano is usually made of iron.