  The two-fluid model of liquid helium is generalized to the case that the
superfluid fraction has a small entropy content. We present theoretical
arguments in favour of such a small superfluid entropy. In the generalized
two-fluid model various sound modes of He$\;$II are investigated. In a
superleak carrying a persistent current the superfluid entropy leads to a new
sound mode which we call sixth sound. The relation between the sixth sound and
the superfluid entropy is discussed in detail.
