Acoustics – Intuitive Understanding of the Unit kg/s^3 for Sound Volume

Question

I know that decibels are used to measure volume of sound, and they are basically a logarithm of $kg/s^3$. The best explanation that I have for the unit of $kg/s^3$ is that it is an alternate way of saying $W/m^2$, which measures intensity of sound. What is an intuitive explanation for the unit $kg/s^3$? What do the kilograms and each factor of a second represent? Is it a way of measuring the variation in how many kilograms of air are hitting your ear every second?

Answer 1

Not every combination of base units has a clear physical meaning. The best way to understand any quantity is to look at the equation that produces it. For instance in your case sound intensity $I$ is an expression of the power $P$ traveling through a perpendicular area $A$,

$$I=\frac P A$$

So you correctly stated that the most natural unit for this is $\rm{W/m^2}$. I could choose to write this equivalently as $\rm{kg/s^3}$ or $\rm{kg \cdot Hz^3}$ or $\rm{eV/(millenia \cdot acre)}$. The units do not provide the meaning. What matters is the physical relationship, expressed in the equation.