||We study waves and oscillations in magnetic structures, e.g., sunspot, fibrils, etc. by analyzing the high-resolution spectral observations provided by the Fast Imaging Solar Spectrometer (FISS) and Interface Region Imaging Spectrograph (IRIS). A bisector method is applied to spectral observations to construct chromospheric Doppler velocity maps. Temporal sequence analysis of these shows enhanced high-frequency oscillations inside the sunspot umbra. Their peak frequency gradually decreases outward from the umbra. The oscillation power is found to be associated with magnetic-field strength and inclination, with different relationships in different frequency bands. We find that the fibrils in the superpenumbra of a sunspot are powered by sunspot oscillations. We find patterns of outward propagation that apparently originate from inside the sunspot, propagate like running penumbral waves, and develop into the fibrils. Redshift ridges seen in the time–distance plots of velocity often merge, forming a fork-like pattern. The predominant period of these shock waves increases, often jumping with distance, from 3 minutes to 10 minutes. This short-to-long period transition seems to result from the selective suppression of shocks by the falling material of their preceding shocks. Based on our results, we propose that the fibrils are driven by slow shock waves with long periods that are produced by the merging of shock waves with shorter periods propagating along the magnetic canopy.