The field-theoretic momentum of longitudinal vibrations in an elastic medium is not the same as the total momentum of the particles which constitute the medium. In this article, we discuss the connection between these two quantities in terms of a new conservation law which follows from an underlying symmetry of the system. The surprising feature of this conservation law is that it is expressed in terms of variables which refer to the medium only, and yet remains valid under a very wide class of couplings of the medium to external systems. The analysis is carried out within the context of a simple one-dimensional model which is easily generalized to three dimensions.

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