The Prandtl–Glauert transformation assumes linearity (i.e. a small change will have a small effect that is proportional to its size). This assumption becomes inaccurate toward Mach 1 and is entirely invalid in places where the flow reaches supersonic speeds, since sonic shock waves are instantaneous (and thus manifestly non-linear) changes in the flow. Indeed, one assumption in the Prandtl–Glauert transformation is approximately constant Mach number throughout the flow, and the increasing slope in the transformation indicates that very small changes will have a very strong effect at higher Mach numbers, thus violating the assumption, which breaks down entirely at the speed of sound.