Question

Phase difference between pressure variation and particle displacmenet

Answer 1

Your original equation is missing the amplitude in front of the exponential. It should be something like s(t,x)=s0ej(−ωt+kx) The pressure wave has an amplitude given by the formula above (answer by DumpsterDofus) and a phase shift of 90 degrees relative to the displacement. So you have all you need to write the equation for the pressure wave.