Shock Wave Formation at a Caustic

The behavior of a weak acoustic compression near a caustic surface has been determined for a special class of specified incoming signals. This problem arises in various contexts, including the propagation of sonic booms generated by supersonic aircraft. The solution derives from a mapping of hodograph-like solutions to the physical plane. The maximum amplification for this class of signals of fixed amplitude depends on the width of the incoming signal. The solutions contain reflected shock waves that satisfy the appropriate shock jump conditions, provided the width of the incoming signal is greater than a certain critical value.