Relationship of Mass Source and Density in a Acoustic Wave Propagation

When trying to solve the harmonic acoustic wave propagation in a pipe in time domain - is there any relationship between P and Mass source excitation transient Q? It looks to be different than Q = 2P/C. 

Regarding transient analyses, the mass source term becomes mass source rate, meaning it has units of kg/m/s^2 (over an area), so one would take the time derivative of Q (e.g., if Q=Qo exp(jwt) and Qo=2*rho/c, then the mass source rate is :  dQ/dt or Qo*jw*exp(jwt)   when constructing the time-history loading).