The fixed phase constant 𝜙ϕ\phi is new; it describes what the wave looks like at (𝑥=0,𝑡=0)(x=0,t=0)(x=0,t=0). The symbol ±±\pm asks us to choose +++ or −−-, which describes the direction that the wave travels.

𝐴AA is always positive.

In most material waves we typically encounter, the "shape" of the disturbance stays the same over short travel distances.

All the heat the enters the system which is free, the heat added will go into the work being done by the gas at it expands

balanced