We study the variation in plasma beta, Alfven Mach number, and magnetosonic Mach number during different geomagnetic storms of solar cycles 23, 24, and 25. In addition, we employ measurements of the solar wind’s flow pressure, proton density, interplanetary magnetic field (IMF) along the z-direction (Bz), temperature, velocity, and geomagnetic index SYM-H. Here, the wavelet coherence (WTC) approach of plasma beta, the Alfven Mach number, and the magnetosonic Mach number have been used with the symmetrical H component (SYM-H) index, which are critical indicators of the plasma behavior and magnetic field interactions. A solar CME or, much less severely, a corotating interaction region (CIR), which is formed at the leading edge of a high-speed stream, is the source of the magnetic storm. The key objective of this study is to reveal the possible dependencies of the geomagnetic indices on whether a storm is driven by a CME or CIR. For CIR-associated storms, large amplitude waves occur preferentially with the rising Alfven Mach number and plasma beta. At the same time, the magnetosonic Mach number lacks variability during the storms caused by shock on the arrival of Earth’s environment. This is different for CME-driven storms, where the variations of the magnetosonic Mach number do not show much fluctuation compared to the Alfven Mach number and plasma beta. WTC between SYM-H and our derived parameters indicates periodicities between 64 and 512 minutes and noticeable regions of significantly enhanced power on November 07–09, 2004, and June 21–23, 2015. However, the magnetosonic Mach number showed a noticeable coherence with SYM-H between 64 and 250 minutes on September 06–08, 2017. Although, during March 19–21, 2021, both the Alfven Mach number and magnetosonic Mach number showed a noticeable coherence with SYM-H, plasma beta showed none. These parameters can be used in the prediction of geomagnetic storms of the category above G3.