We present universal formulas for the spectral and temporal output optical fields from a linear traveling-wave medium whose refractive index changes during its propagation within the medium. These formulas agree with known changes in central wavelength and energy that are associated with adiabatic wavelength conversion (AWC). Moreover, they reveal new changes to the optical pulses that have not been noticed, such as pulse compression and spectral broadening. Most significantly, we find that AWC alters the pulse power, pulse chirp, and pulse delay. All of these effects depend on whether the central wavelength is blueshifted or redshifted, the first sign of asymmetry to be reported for AWC. These findings impact the applications of AWC to optical signal processing in microphotonic and nanophotonic structures as well as in lightwave systems.