L-Tryptophan is an extremely important amino acid for a variety of biological functions in living organisms. In this study we were able to measure changes in the concentration of L-tryptophan when incorporated into pellets with polyethylene as a host. The changes were measured both through the characteristic absorption bands of the C11 and C12 bonds in the low terahertz frequency range and using changes in the refractive index where pellets with higher concentrations of L-tryptophan showed higher refractive indices. The volumetric concentration of L-tryptophan in the polyethylene pellet was accurately determined with a simple model that explains the contribution to the complex refractive index for the resultant sample due to the two constituent materials. These measurements show that terahertz time-domain techniques can be applied to detect variation in concentration of certain amino acids rapidly by examining the relative phase delay and amplitude change of the terahertz transients.