Visualise the sound intensity I'm studying Biophysics and my current subject is sound. One of the properties of sound is intensity. From my notes I can see the following definition:
Intensity Formula is: $(I = w*m^{-2})$ or $(I = \frac{w}{m^2})$ where w = amound of energy and m = area.
Definition: Intensity is the amount of energy passing through an area of $1m^2$ perpendicular to the direction of sound wave propagation within 1 second.
So I came with this picture:

I know the picture is lame. What I care about is if the above definition is diplayed correctly here. I'm not a native English speaker and the word perpendicular in this context confuses me.
Thanks
 A: Please note that the original definition of intensity does not in any way declare the "size" of the dimensions. The definition of intensity, as you have already stated is
$$ I = \frac{P}{A} \tag{1}\label{1} $$
where $P$ is power (energy over time) and $A$ is area.
Now, there's absolutely no restriction as to what the size of the area should be. You could very well measure the power passing perpendicularly through an area of ten square kilometres and then do the reduction to an area of one metre. This, of course, presupposes that the sound field is constant (both in magnitude and direction) through this surface.
This is used in practice in the other way around. You measure in a very small area where you suppose that the field is constant and then convert the result to the S.I. system (or any other system you use).
For example, let's assume that you measure with a device (this could be a microphone) the pressure of the sound field at a point and by analogy to the intensity for a point source
$$ I = \frac{p^{2}}{\rho c} \tag{2}\label{2} $$
with $p$ denoting the sound pressure, $\rho$ the density of the medium ($\rho \approx 1.204 \frac{kg}{m^{2}}$ for air for temperature $T = 20 ~ ^{o} C$) and $c$ the speed of sound (in air $c \approx 343 \frac{m}{s}$ for temperature $T = 20 ~ ^{o}C$) you can estimate the intensity passing through that point. If you know the area of the microphone diaphragm, you could use that too to get a better approximation.
Obviously, this last method is just an "engineering approximation" where you first of all consider an ideal point (omnidirectional) source and free field conditions, so that all energy impinging on the microphone diaphragm results solely from the radially outward intensity component of the source.
For better results, one should use intensity probes. The simplest of those are made from pairs of matched microphones at specific distances apart where the pressure differential is used to estimate the particle velocity, which in turn is a vectorial quantity showing the direction of propagation. Then the equation giving the intensity, eq. \eqref{3} is used to calculate the intensity passing through the normal of the intensity probe.
$$ I = p \vec{u} \tag{3} \label{3} $$
Please note that there are various different methods to measure the sound intensity (or at least an approximation of it). For more information on sound intensity I encourage you to get a hands on the textbook "Sound Intensity" by Frank Fahy. There is no intend to advertise the reference, it just happens to be my own personal favourite for this topic. Please feel free to look for the topic in any other reference you may prefer.
