Knowledge of dispersion and attenuation is essential for better reservoir characterization and hydrocarbon identification. However, limited by reliable laboratory data at seismic frequency bands, the roles of rock and fluid properties in inducing dispersion and attenuation are still poorly understood. Here we perform a series of laboratory measurements on two sandstones under both dry and partially water-saturated conditions at frequencies ranging from 2 to 600 Hz. Two samples, Bentheimer and Bandera sandstones, have similar porosity of $\sim$20% but different permeability of 1830 mD and 33 mD. At vacuum-dry conditions, the bulk dispersion and attenuation in Bandera sandstone with more clay contents are distinctly larger than those in Bentheimer sandstone, suggesting clay contents might contribute to the inelasticity of the rock frame. The partially water-saturated results show the combined effects of rock permeability and fluid saturation on bulk dispersion and attenuation. Because of the high compressibility of gas, even a few percent of gas ( $\sim$5%) can substantially dominate the pore-fluid relaxation by providing a quick and short communication path for pore pressure gradients. The consequent bulk dispersion and attenuation are negligible. However, when the sample is approaching a fully water-saturated condition (gas saturation $<$5%), the gas effect gradually decreases. Instead, the rock permeability begins to play an essential role in the pore-fluid relaxation. For Bandera sandstone with lower permeability, a partially relaxed status of pore fluids is achieved when the gas saturation is lower than 5%, accompanied by significant attenuation and dispersion.