  The equation of the Doppler shift of two bodies in inertial motion in a
reference frame at rest (i.e., stationary reference frame) is derived. In this
derivation, the wave-particle duality of photons in the theory of special
relativity is considered. The dilation of time of a moving clock, which is
derived from the Lorentz transformation that depends on the velocity of the
moving clock in the reference frame at rest, and wavefront counting by
geometrical drawing are used to describe the longitudinal Doppler shift. We
show that the equation of the Doppler shift depends on the velocities of the
two bodies in the reference frame at rest.
