The measurable physical quantities given by special relativity show a significant difference from the results of classical Newtonian mechanics at high speeds, but they are generally compatible with classical Newtonian mechanics at low speeds, meaning that the Lorentz transformation degenerates into the Galilean transformation in the low-speed limit. Such compatibility is consistent with the reality, but also makes it difficult to verify the special relativity in the low speed limit. However, the Doppler effect has a distinct gap between the Lorentz transformation and the Galilean transformation even at low speed, which provides a possible route to verify the special relativity at the low speed. By using two coherent laser lights after Doppler red/blue shift, their superposition will lead to the beat frequency effect. By monitoring the value of the beat frequency, the Lorentz transformation and the Galilean transformation can be significantly distinguished under low-speed conditions. The above function can be achieved by modifying the Michelson interferometer.