[Betsy, Travis, Gabriele]

Yesterday afternoon and this morning we measured the in-air violin mode frequencies at ETMX. We followed the same procedure described in 38857, 38742 and T1700430. Some details of the measurement parameters:

• We used a SR785, acquiring the X channel of the QPD, input level at 0 dBm. 
• The soruce was set at 40-70mV peak (depending on the mode), using band-limited white noise
• 20 averages, each FFT was 32s long (25 Hz bandwidth around the central peak frequency, 800 lines, corresponding to an analyzer bandwidth of 31.25 mHz)
• We noticed that when the chamber door was completely closed with the cloth, air turbulence made the measurement worse
• We measured up to the 3rd harmonic of each fiber

The results are shorn in the first plot. Clearly all peaks show a lot of sidebands (likely due to low frequency motion of the suspension). The plot also shows the bst fit with a Lorentzian curve (plus constant background), using a frequency bandwidth of 3 Hz around the peak. As you can see, some of the measurements are better than others...

In the table below we report the central frequency for each mode and the width of the Lorentzian peak fitted to the data. The error in the peak frequency is NOT the Lorentzian fit width, but it is obtained from a MCMC fit of the data, using a model that includes as parameters: the peak frequency, the peak width, the background level, and a constant but unknown measurement error for the spectrum in each frequency bin. The quoted uncertainty is the 90% percentile after marginalization over all parameters but the peak frequency. Since the uncertainties computed in this was are smaller than the analyzed bandwidth, they might be an underestimate. The attached PDF files show the corner plots for all fits.