Sound pressure level(SPL), sound power and sound intensity are analogous to temperature, heater power and heat flow for a heater:
- The temperature (deg C), which varies by location in the room, can be expressed by just a number (scalar) at that location. Just like SPL.
- the heater power (Watts), which doesn't depend on where the heater is placed, is also just a number. Just like sound power. When you put 500 electrical Watts into a sub, 5 Watts of sound power comes out and the 495 Watts make the sub get hot.
- the heat flows around the room so as it travels, it has a measurable power AND direction (vector). This heat's magnitude and direction can be measured as it flows over a specific area (Watts/square meter) just like sound intensity.
In pictures, sound power is a number AT the sub's driver. SPL is a scalar field represented by a number at each location in the room. Sound intensity is a vector field represented by a number AND direction at each location in the room.
I can tell you discrete, per-channel subs in my room sound and feel like multiple, large, channel-specific vectors.
