[en] The problems related to the choice of phase velocity of waves in irregular waveguides when solving the problems of synthesis that allow to determine the waveguide geometric parameters by the given output parameters of a charged particle beam in waveguide electron and proton accelerators or the output power of the electromagnetic radiation field in travelling wave generators and amplifiers are considered. Phase coefficients of the waves of the effective electromagnetic field, which is the sum of the field excited by the beam and the generator field, are determined. The expressions obtained for the phase velocity of waves in a waveguide allow estimates for limiting values of radiation currents and rates