In the first part of the paper, a model of the physical system based on the previously proposed approach was developed. The model assumes that the observers cannot be separated from phases of waves U = cos kγ(x − βat) cos kγ(at − βx) propagating in an infinite homogeneous string. It was shown that there was a time dilation effect of the moving observer, similar to the effect known from the theory of relativity. In the second part, a new reference system K′ is constructed on the basis of the wave U. In this system, U is a standing wave; its oscillations are in phase and serve as a standard of simultaneity in various points of the system. Period of oscillation and wavelength of U are standards of time interval and of length for the system. Phases kγ(x − βat) are identified with the observers, and the oscillations described by the function cos kγ(at − βx) act as “biological processes” of observers. Manifestations of the principle of relativity in this model are discussed in details. It is shown that the system K′ has no “aether wind”. The Lorentz transformations for linking the coordinates of the event observed from the laboratory reference system with coordinates of the system K′ were derived without the explicit use of the theory of relativity postulates. The model of standing waves illustrates the relativity of simultaneity, the relativity of length contraction and time dilation, the twin paradox, and the invariance of the speed of sound.