### 11.1 Single fluid case

Suppose that there is only one constituent, with index . The master function then
depends only on . The variation in the chemical potential due to a small disturbance is
where
The equation of motion is . It is not difficult to show, by using the condition of transverse wave
propagation (188) and contracting with the spatial part of the wave vector , that the equation
of motion reduces to
The speed of sound is thus
Given that a well-constructed fluid model should have , we see that the second term must be
negative. This would ensure that the model is causal.