The domain occupied by the waveguide is a strip with n+1 equal narrows of diameter ϵ. The wave function of a free electron satisfies the Dirichlet boundary value problem for the Helmholtz equation. Any part of the waveguide between two neighboring narrows plays the role of a resonator. Near a simple eigenvalue of the closed resonator, there are n resonant peaks of height close to 1. We let (Formula presented.) and obtain asymptotic formulas for the resonant values of the spectral parameter and for the widths of the resonant peaks at their half-height. The behavior of the transmission coefficient in a neighborhood of a resonance is described.