First, you need to define the base frequency and variance respect to that. We also set nLight to indicate the number of waves we are adding up.

ω0=1;dωratio=.1;nLight=100;

Next, we make a random list of frequencies that are sampled from a Gaussian centered at ω0 and with width dωratio.

ωlist= Table[RandomVariate[NormalDistribution[ω0,dωratio*ω0]] ,nLight];

Finally, we can plot the sum of the waves. Note that 
Table[Cos[ωlist[[i]] t],{i,1,nLight}]
generated the list of all the waves and then 
Total
adds them up. We also normalize it for simplicity.

Plot[1/nLight*Total[Table[Cos[ωlist[[i]] t],{i,1,nLight}]],{t,0,40π},PlotRange->All]