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At high speeds, the grooves cut into car tire treads can be rapidly squeezed and suffer volume losses of around 10%. This decrease in groove volume can occur much faster than air can evacuate from the squeezed groove as ground impact causes the groove walls to move with velocities of order 1m/s, and with accelerations of 103m/s2over time scales of about 1ms. The resulting volume loss without any accompanying evacuation of air leads to significant increases in pressure and density in the groove. The pressure fluctuations can exceed 10% of ambient conditions which makes the usual approximations underlying use of the acoustic wave equation invalid. The acoustic wave equation can only be used when pressure fluctuations and pressure gradients are small. When substantial pressure fluctuations exist or when shock waves are present the usual acoustic wave equation cannot be used and a fuller treatment is required. This paper presents preliminary analytical and numerical investigations of the various nonlinear effects which might create novel acoustic sources from squeezed cavities in car tires.