Acoustic metric

In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties characteristic of a given particulate medium in acoustics, or in fluid dynamics. Other descriptive names such as sonic metric are also sometimes used, interchangeably. In mathematical physics, a metric describes the arrangement of relative distances within a surface or volume, usually measured by signals passing through the region – essentially describing the intrinsic geometry of the region. An acoustic metric will describe the signal-carrying properties characteristic of a given particulate medium in acoustics, or in fluid dynamics. Other descriptive names such as sonic metric are also sometimes used, interchangeably. For simplicity, we will assume that the underlying background geometry is Euclidean, and that this space is filled with an isotropic inviscid fluid at zero temperature (e.g. a superfluid). This fluid is described by a density field ρ and a velocity field v → {displaystyle {vec {v}}} . The speed of sound at any given point depends upon the compressibility which in turn depends upon the density at that point. This can be specified by the 'speed of sound field' c. Now, the combination of both isotropy and Galilean covariance tells us that the permissible velocities of the sound waves at a given point x, u → {displaystyle {vec {u}}} has to satisfy This restriction can also arise if we imagine that sound is like 'light' moving though a spacetime described by an effective metric tensor called the acoustic metric.