Data to attempt fit for the structure damped phi of the steel music wire

Material constants used to estimate Zener damping

   E = Young's modulus =  1.76 x 10^12 dynes/cm^2

   alpha = expansion coeff = 1.1 x 10^-5 1/K

   C = heat capacity = 3.5 x 10^7 ergs/cm^3K

   K = thermal conductivity = 4.6 x 10^6 ergs/sec cm K

   d = diameter of wire = 3.048 x 10^-2 cm

   f0 = Zener relaxation frequency = 306Hz

   del = Zener amplitude = 1.88 x 10^-3   

   m = mirror mass = 1.02 x 10^4 gm

   g = acceleration of gravity = 980 cm/sec^2

   df = dilution factor = 5.4 x 10^-3

   L = pendulum length = 45 cm


Data for wire Q at fundamental and 3 harmonics

   f Hz   1/Q           df*phi(zener)   (1/Q - df*phi(zener))
                                 
  330    8.33 x 10^-6   4.93 x 10^-6      3.4 x 10^-6      

  660    6.67 x 10^-6   3.77 x 10^-6      2.9 x 10^-6

  990    5.88 x 10^-6   2.79 x 10^-6      3.1 x 10^-6

 1320    5.26 x 10^-6   2.17 x 10^-6      3.1 x 10^-6

The residual phi divided by the dilution factor is on average

    delta = 5.7 x 10^-4

This is larger than the loss in the unloaded wire measured by Steve Penn by
about a factor of 5 to 10. Since the clamp and the double prism give almost identical
loss at 330 Hz, it is most likely not the loss in the wire but rather an additional
loss in the setup. We did not chase this further being happy with the high Q value
and its constancy.


Definition of the dilution factor

             2        EI
   phi(f) = ----sqrt(------) phi0(f) = df phi0(f)
             L        Mg/2

  E = Young's modulus
  I = moment of inertia of the area  = pi*a^4
                                       ------
                                         4
  L = pendulum length


Zener damping

                   wtau
   phi(f) = del--------------
                  1 + (wtau)^2

   del = E alpha^2 T/C

   f0 = 1/2pi*tau = 2.16 Kth/Cd^2  
  
    d = wire diameter
    Kth = thermal conductivity
    C = heat capacity per unit volume