In the past, roughness effects were included in models by using various friction laws. In contrast, this study deals with simple Poisson impact and Coulomb friction laws on multiple concurrent contacts between geometrically random rough surfaces and their effect on the slider's roughness-induced vibrations. The closed-form solutions derived here relate roughness-induced vibrations to the surface roughness, slider mass, slider load, slider dimensions, relative sliding speed, and the coefficient of restitution. Wear influences were studied by simulating random rough surfaces with multiple concurrent contacts. Contrary to expectations we found that random roughness can induce slider vibrations of distinct frequencies. We found a good agreement between the results of the studied models and the experiments. The closed-form solution was found to be suitable for estimating the roughness-induced vibration frequencies of a hard-disk drive's writing/reading head and those of a car-brake's pad (known as squeal-noise).