A towed array is modeled as a periodic arrangement of identical fluid‐filled hose modules supporting two types of longitudinal waves —extensional waves in the hose wall and resonant breathing waves in the hose‐and‐fluid combination [D. Chase, BBN Rep. 2408 (1972)]. These waves are coupled at the module termini (end shells) where velocities in both types of waves coincide. The net force on an end shell is the sum of forces due to the arrival of both types of waves generated by vibrations of the two adjacent end shells. This dual‐wave model is analogous to a system of masses connected by two springs of different stiffness. End shell motions are described by a superposition of “velocity amplitude waves” of frequency‐dependent phase velocity propagating through them. If resonant breathing waves are lightly damped, in certain frequency intervals these waves are highly damped due to force cancellation. Within such stop bands, an array will be quiet in a narrow‐band sense. Many features of measured low‐frequency self noise are predicted by this model. [Supported by Naval Ship Systems Command.]