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Waves and oscillations are important solar phenomena, not only because they can propagate and dissipate energy in the chromosphere, but also because they carry information about the structure of the atmosphere in which they propagate. The nature of the three-minute oscillations observed in the umbral region of sunspots is considered to be an effect of propagation of magnetohydrodynamic (MHD) waves upward from below the photosphere. We present a study of sunspot oscillations and wave propagation in NOAA AR 12470 using an approximately one-hour long data set acquired on 2015 December 17 by the Atacama Large Millimeter/submillimeter Array (ALMA), the Goode Solar Telescope (GST) operating at the Big Bear Solar Observatory (BBSO), the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO), and the Interface Region Imaging Spectrograph (IRIS). The ALMA data are unique in providing a time-series of direct temperature measurements in the sunspot chromosphere. The two-second cadence of ALMA images allows us to well resolve the three-minute periods typical of sunspot oscillations in the chromosphere. Fourier analysis is applied to ALMA Band 3 ($\sim$100 GHz, $\sim$3 mm) and GST H$\alpha$ data sets to obtain power spectra as well as oscillation phase information. We analysed properties of the wave propagation by combining multiple wavelengths that probe physical parameters of solar atmosphere at different heights. We find that the ALMA temperature fluctuations are consistent with that expected for a propagating acoustic wave, with a slight asymmetry indicating non-linear steepening., Comment: 18 pages, 13 figures

We present observational constraints on the solar chromospheric heating contribution from acoustic waves with frequencies between 5 and 50 mHz. We utilize observations from the Dunn Solar Telescope in New Mexico complemented with observations from the Atacama Large Millimeter Array collected on 2017 April 23. The properties of the power spectra of the various quantities are derived from the spectral lines of Ca II 854.2 nm, H I 656.3 nm, and the millimeter continuum at 1.25 mm and 3 mm. At the observed frequencies the diagnostics almost all show a power law behavior, whose particulars (slope, peak and white noise floors) are correlated with the type of solar feature (internetwork, network, plage). In order to disentangle the vertical versus transverse plasma motions we examine two different fields of view; one near disk center and the other close to the limb. To infer the acoustic flux in the middle chromosphere, we compare our observations with synthetic observables from the time-dependent radiative hydrodynamic RADYN code. Our findings show that acoustic waves carry up to about 1 kW m$^{-2}$ of energy flux in the middle chromosphere, which is not enough to maintain the quiet chromosphere, contrary to previous publications., Accepted for publication in ApJ