Waves carry energy and as the wave travels outward, that energy is spread out over a larger space. How loud a sound is depends not only on the energy put in by the source but also the distance between the source and the observer and the medium through which the sound travels.
XMphysics answers the question, what is wave intensity?
Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.
Waves require energy to be created and they carry that energy as they travel outward. Along the way that energy can become dissapated, usually because the space it occupies increases. Friction from the medium can add additional effects that absorb the wave's energy, decreasing the energy density at a given spot - for now, lets disregard those effects. For a spherical wave, like most sound and light waves, this effect can be visualized by the wave spreading from the source to fill the room.
Here the intensity, which is the power (Watts) per unit area, decreases as you move away from the source.
$P=\frac{energy}{time}$
$I = \frac{P}{A}$, where $A$ is the area over which the energy is spread
For a spherical wave, the energy is spread over the surface of a sphere. $A_{sphere}=4 \pi r^2$. So the intensity decreases inversely on the square of the distance from the source. This is an important physical observation, the so called inverse square law, also found in the universal law of gravity and in the interaction of charged particles.
Its common to consider the source producing some power (usually constant) that generates a wave, which decreases in intensity as it moves away from the source. That intensity then could be used to find the amount of energy per time (power) that is incident on a given region of space. This second power is not that of the source and the area may not be that of a sphere. For example if you have speaker powered by a 10 W source, that power spreads out over an area of $4 \pi r^2$ but then only some of that energy goes through a square window, where $A=l^2$, where $l$ is the length of the side of the window.
The range of human hearing, from the threshold of barely making out a sound, to that of causing damage, spreads 12 orders of magnitude. To deal with these large scales the Decibel scale was introduced. The Decibel Level ($\beta$), measured in dB's, is proportional to the log of the ratio of the intensity to that of the threshold of human hearing, $I_0=10^{-12}\frac{W}{m^2}$.
$\beta=(10dB) log{\frac{I}{I_0}}$
Since the intensity $I$ depends on the power of the source, and distance between the source and the observer, the Decibel level also depends on those quantities.
Now, take a look at the pre-lecture reading and videos below.
