Here, reduction in acoustic noise due to insertion of thin reflecting barriers has been estimated. Accurate simulations have been performed using numerical methods with a near spectral resolving ability, neutral stability and the physical dispersion relation preserving ($DRP$) nature. Use of high accuracy schemes makes present approach useful in analysis of an acoustic field consisting of acoustic waves with a large frequency band. Present investigation has been carried out for eight geometrically different acoustic barriers and for nine discrete frequencies in the one-third octave band starting from 250 $Hz$ to 1600 $Hz$. Use of high accuracy $DRP$ scheme allows one to compute the complex acoustic field by accurately capturing reflection, diffraction and interference of acoustic waves. Comparison of numerically obtained sound pressure level ($SPL$) distributions at different heights with the available experimental results in the literature shows a good match for the case of $I$-shaped barrier. In order to quantify effects of acoustic source frequencies over a large band, we have extended our analysis for a frequency range of 100 $Hz$ to 5000 $Hz$ for the case of $I$-shaped barrier. Present analysis shows that the thick $T$-shaped barrier and grooved barrier work efficiently in the low and mid frequency range while in the higher frequency range all the barriers are equally effective due to minimal diffraction.