  We investigate interacting phase oscillators whose mean field is at a
different frequency from the mean or mode of their natural frequencies. The
associated asymmetries lead to a macroscopic travelling wave. We show that the
mean ensemble frequency of such systems differs from their entrainment
frequency. In some scenarios these frequencies take values that,
counter-intuitively, lie beyond the limits of the natural frequencies. The
results indicate that a clear distinction should be drawn between the two
variables describing the macroscopic dynamics of cooperative systems. This has
important implications for real systems where a non-trivial distribution of
parameters is common.
