These are fluctuations in air pressure that were theorised in 1937 but have never proven to occur in nature, until now.
The study was published in the Journal of the Atmospheric Sciences.
The eruption in January released what was likely the most powerful explosion the world has experienced since the 1883 eruption of Mt Krakatau in Indonesia.
The rapid release of energy excited pressure waves in the atmosphere that quickly spread around the world.
Similar behaviour to famous Krakatau eruption
The researchers said the atmospheric wave pattern close to the eruption was quite complicated, but thousands of kilometres away the disturbances were led by an isolated wave front travelling horizontally at more than 1000km/h as it spread outward.
The air pressure perturbations associated with the initial wave front were seen clearly on thousands of barometer records throughout the world.
"The same behaviour was observed after the Krakatau eruption, and in the early 20th century a physical theory for this wave was developed by the English scientist Horace Lamb," said Kevin Hamilton, emeritus professor of atmospheric sciences at the UH Mānoa School of Ocean and Earth Science and Technology.
"These motions are now known as Lamb waves. In 1937, the American-Israeli mathematician and geophysicist Chaim Pekeris expanded Lamb's theoretical treatment and concluded that a second wave solution with a slower horizontal speed should also be possible.
"Pekeris tried to find evidence for his slower wave in the pressure observations after the Krakatau eruption but failed to produce a convincing case."
Scientists applied a broad range of tools now available, including geostationary satellite observations, computer simulations and extremely dense networks of air pressure observations, to successfully identify the Pekeris wave in the atmosphere following the Tonga eruption.
Lead author Shingo Watanabe performed computer simulations of the response to the Tonga eruption.
"When we investigated the computer-simulated and observed pulses over the entire Pacific basin, we found that the slower wave front could be seen over broad regions and that its properties matched those predicted by Pekeris almost a century ago," Hamilton said.