Raman spectroscopy is used to study magnetic excitations in the quasi one dimensional $S=1/2$ quantum spin systems Cu(Qnx)(Cl$_{1-x}$Br$_x$)$_2$. The low energy spectrum is found to be dominated by a two-magnon continuum as expected from the numerical calculations for the Heisenberg spin ladder model. The continuum shifts to higher energies as more Br is introduced. The cutoff of the scattering increases faster than the onset indicating that the increase of exchange constant along the leg is the main effect on the magnetic properties. The upper and lower continuum thresholds are measured as a function of Br content across the entire range and compared to estimates based on previous bulk studies. We observe small systematic deviations that are discussed.
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