Koji suggested that I make a cosine fit for the curve instead of a linear fit.

I fit the data to  
where L - cable length asymmetry (27 cm) , f_b - beat frequency and v - velocity of light in the cable (2*10⁸ m/s)

The plot with the cosine fit is attached. 

Fit coefficients (with 95% confidence bounds):
       A =      0.4177  (0.3763, 0.4591)
       B =       2.941  (2.89, 2.992)