Atmosphere above sunspots is abundant with different types of waves. Among these waves are running penumbral waves in the chromosphere, quasi-periodic oscillations in the lower coronal loops, and recently reported running waves in sunspots’ photosphere, all of which were interpreted as magnetoacoustic waves by some authors. Are these waves in different atmospheric layers related to each other, what is the nature of these waves, and where are the ultimate sources of these waves? Applying a time–distance helioseismic analysis over a suite of multi-wavelength observations above a sunspot, we demonstrate that the helioseismic p-mode waves are able to channel up from the photosphere through the chromosphere and transition region into the corona, and that the magnetoacoustic waves observed in different atmospheric layers are a same wave originating from the photosphere but exhibiting differently under different physical conditions. We also show waves of different frequencies travel along different paths, which can be used to derive the physical properties of the atmosphere above sunspots. Our numerical simulation of traveling of waves from a subphotospheric source qualitatively resembles the observed properties of the waves and offers an interpretation of the shapes of the wavefronts above the photosphere.