This paper aims to address a simple but fundamental question, how the traffic oscillations grow along the road. Firstly, we conduct an empirical study on the growth pattern of traffic oscillations on US-101 Freeway and German-A5 Freeway. Then we perform an experiment to study the growth pattern of traffic oscillations on a single lane with a fixed bottleneck of speed limit. Both empirical and experimental results show that traffic oscillations grow in a concave way along the road. This finding is consistent with the previous one that traffic oscillations grow concavely along the platoon following a slower leader taking on the role of a moving bottleneck, which is not to be expected a priori for a fixed bottleneck. Finally, we use the finding to test three typical car-following models. The test indicates that whereas the intelligent driver model (IDM) fails to reproduce the observed growth pattern, the 2D-IDM and the stochastic speed adaptation model could. These findings are expected to improve our understanding of the role of stochasticity in car following, and the high-quality data in itself can be used to test traffic flow models and theories.