Distinctions between boundary and distributed damping in a waveguide with a cutoff frequency

The precise, closed-form solution for response of a finite one-dimensional waveguide with cutoff (string on an elastic foundation) is examined for cases where damping is either uniformly distributed or concentrated in the ends. No marked spatial concentration of response at the driven point is found unless the damping is distributed and also the wave attenuation in one round trip through the system is large. Increased dispersion, as frequency approaches the cutoff, increases the round-trip attenuation caused by distributed viscous damping, but it decreases the attenuation caused by boundary damping (at the ends of the waveguide).