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Context.The elemental abundance in the solar corona differs from that in the photosphere, with low first ionization potential (FIP) elements showing enhanced abundances, a phenomenon known as the FIP effect. This effect is considered to be driven by ponderomotive forces associated with magnetohydrodynamic (MHD) waves, particularly incompressible transverse waves. Aims.We aim to investigate the relationship between coronal abundance fractionation and transverse MHD waves in the chromosphere. We focus on analyzing the spatial correlation between the FIP fractionation and these waves, while exploring wave properties to validate the ponderomotive-force-driven fractionation model. Methods.We analyzed the Hαdata from the Fast Imaging Solar Spectrograph of the Goode Solar Telescope to detect chromospheric transverse MHD waves, and Si X(low FIP) and S X(high FIP) spectra from the EUV Imaging Spectrometer on board Hinode to determine the relative abundance in an active region. By extrapolating linear-force-free magnetic fields with Solar Dynamics Observatory/Helioseismic and Magnetic Imager magnetograms, we examine the connection between chromospheric waves and coronal composition. Around 400 wave packets were identified, and their properties, including the period, velocity amplitude, propagation speed, and propagation direction, were studied. Results.These chromospheric transverse MHD waves, mostly incompressible or weakly compressible, are found near loop footpoints, particularly in the sunspot penumbra and superpenumbral fibrils. The highly fractionated coronal region is associated with areas where these waves were detected within closed magnetic fields. Our examination of the statistics of wave properties revealed that downward-propagating low-frequency waves are particularly prominent, comprising about 43% of the detected waves. Conclusions.The correlation between abundance fractionation and transverse MHD waves, along with wave properties, supports the hypothesis that FIP fractionation occurs due to the ponderomotive force from transverse MHD waves in the chromosphere. Additionally, the observed characteristics of these chromospheric waves provide valuable observational constraints for understanding the FIP fractionation process.