The paper addresses the propagation of waves in a pipe of small diamet
er compared to the sound wavelength with an insert of a waterlike mate
rial (rubber). It is shown that this structure can sustain two propaga
ting modes, high-velocity and low-velocity. The high-velocity mode pro
pagates at a velocity close to that of sound in water. The low-velocit
y mode propagates at a velocity close to that of longitudinal waves in
a waterlike rod. Consideration is given to a sound muffler design whi
ch depends for its operation on the interference of the two modes.