\(v_{boom}=3.4354*\cfrac{2.196*10^{3}}{14+8*2}=251.47\,ms^{-1}\)
\(T_{boom}=251.47^2*\cfrac{60.08*10^{-3}}{3*8.3144}=152.32\,K\) or \(-120.83\,^{o}C\)
\(T_{p}=251.47^2*\cfrac{60.08*10^{-3}}{2*8.3144}=228.48\,K\) or \(-44.67\,^{o}C\)
neither of which is tempering temperature of about \(620\,^{o}C\).
We don't have a speculative relation between \(T_{boom}\) and glass tempering.
If we focus on only the silicon atoms in the structure and adjust both density and molar mass accordingly,
adjusted density, \(\rho_{adj}=2.196*\cfrac{28.1}{28.1+16*2}=1.027\,gcm^{-3}\)
adjusted molar mass, \(M_{adj}=60.08*\cfrac{28.1}{28.1+16*2}=28.09\,g\,mol^{-1}\)
So,
\(v_{boom}=3.4354*\cfrac{1.027*10^{3}}{14}=252.01\,ms^{-1}\)
\(T_{boom}=252.01^2*\cfrac{28.09*10^{-3}}{3*8.3144}=71.52\,K\) or \(-201.63\,^{o}C\)
there is a slight increase in the value of \(v_{boom}\) but \(T_{boom}\) is of a lower value than previously.
The other significant ingredient in glass is Sodium oxide \(Z=12*2+8\), \(Na_2O\) of density \(2.27\,\,gcm^{-3}\) and molar mass \(61.98\,\,gcm^{-3}\). Both physical properties of which are similar to silicon dioxide.
\(v_{boom}=3.4354*\cfrac{2.27*10^{3}}{12*2+8}=243.70\,ms^{-1}\)
\(T_{boom}=243.70^2*\cfrac{61.98*10^{-3}}{3*8.3144}=147.57\,K\) or \(-125.58\,^{o}C\)
which is too low.
Maybe it is Calcium oxide \(Z=20+8\), \(CaO\) of density \(3.34\,\,gcm^{-3}\) and molar mass \(56.08\,\,gcm^{-3}\) that plays a role in tempering glass,
\(v_{boom}=3.4354*\cfrac{3.34*10^{3}}{20+8}=409.79\,ms^{-1}\)
\(T_{boom}=409.79^2*\cfrac{56.08*10^{-3}}{3*8.3144}=377.55\,K\) or \(104.4\,^{o}C\)
but lime together with aluminium oxide \(Al_2O_3\), and magnesium oxide \(MgO\), are added to counter sodium carbonate \(Na_2CO_3\) that makes glass water soluble. The three additives are to provide for a better chemical durability in glass.
For completeness sake,
Aluminium oxide \(Z=13*2+8*3\), \(Al_2O_3\) of density \(3.987\,\,gcm^{-3}\) and molar mass \(101.96\,\,gcm^{-3}\)
\(v_{boom}=3.4354*\cfrac{3.987*10^{3}}{13*2+8*3}=273.94\,ms^{-1}\)
\(T_{boom}=273.94^2*\cfrac{101.96*10^{-3}}{3*8.3144}=306.75\,K\) or \(33.6\,^{o}C\)
\(v_{boom}=3.4354*\cfrac{3.6*10^{3}}{12+8}=618.37\,ms^{-1}\)
\(T_{boom}=618.37^2*\cfrac{40.304*10^{-3}}{3*8.3144}=617.86\,K\) or \(344.71\,^{o}C\)
Try tempering glass at temperatures given by \(T_{p}\) values for Aluminium oxide (\(186.98\,^{o}C\)) and Magnesium oxide (\(653.65\,^{o}C\)).
Good luck.
