We report in this paper the wavelength switching features of semiconductor ring lasers that are wavelength tunable based on filtered optical feedback. The filtered feedback provides a wavelength dependent loss mechanism in these devices with which a particular longitudinal mode, and thus a particular wavelength, can be selected by changing the filter characteristics of the feedback channel. We investigate how the wavelength switching speed depends on the amplitude of the modulation of the switching driving signal and on the different phase factors within the filtering branches of the SRL. We compare qualitatively the experimental results with numerical simulations based on a travelling wave model. We also investigate the dynamical behavior of the lasing and non-lasing longitudinal modes in the two channels of the clockwise and the counter-clockwise directions. We show the crucial importance of various phase relation factors on the wavelength switching behavior. Finally, we discuss what limits the switching speed and how we can accelerate it.