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High-energy cosmic rays that hit the Earth can be used to study large-scale atmospheric perturbations. After a first interaction in the upper parts of the atmosphere, cosmic rays produce a shower of particles that sample it down to the detector level. The HAWC (High-Altitude Water Cherenkov) gamma-ray observatory in Central Mexico at 4,100 m elevation detects air shower particles continuously with 300 water Cherenkov detectors with an active area of 12,500 m2. On January 15th, 2022, HAWC detected the passage of the pressure wave created by the explosion of the Hunga volcano in the Tonga islands, 9,000 km away, as an anomaly in the measured rate of shower particles. The HAWC measurements are used to determine the propagation speed of four pressure wave passages, and correlate the variations of the shower particle rates with the barometric pressure changes. The profile of the shower particle rate and atmospheric pressure variations for the first transit of the pressure wave at HAWC is compared to the pressure measurements at the Tonga island, near the volcanic explosion. By using the cosmic-ray propagation in the atmosphere as a probe for the pressure, it is possible to achieve very high time-resolution measurements. Moreover, the high-altitude data from HAWC allows to observe the shape of the pressure anomaly with less perturbations compared to sea level detectors. Given the particular location and the detection method of HAWC, our high-altitude data provides valuable information that contributes to fully characterize this once-in-a-century phenomenon.