I and others have touted how volume decreases in direct proportion to the square of the distance with point sources (cone speakers), but only directly to the distance with line sources (i.e., ML speakers). In other words, move twice the distance from a point source and the volume decreases to 1/4, but to only 1/2 for a line source (1/9 vs 1/3 for three times the distance, and so forth). This is not intuitive to most folks, and throwing complicated theory and equations around just confuses things (see this Sound Propagation paper, for example).
Well, I've done a bit of teaching technical stuff to non-technical folks over the years, and I came up with an easier way to describe this to my wife (who is definitely not technical
), and she said "Oh, I see now." So I thought perhaps this approach could be helpful to others.
It goes like this: Sound is simply energy that comes from a speaker, and how much of that energy you receive will determine how 'loud' it is to you (i.e., the volume). Now, for a point source the energy will move out in a sphere, but for a line source it will move out in a cylinder (we'll ignore the 'ends' of the cylinder for this). Finally, the amount of energy available at any point on one of these expanding surfaces (i.e., the volume at a listening position) will be the total energy divided by the total area of that surface that it has to be 'spread over'.
Well, the surface area of a sphere is calculated as "four times PI times R-squared" (I don't know how to do equations here), where R is the radius, while the surface area for a cylinder (again, ignoring the two 'ends') is calculated as "two times R times PI times H", where R is the radius and H is the hight of the cylinder. So you can see that doubling R (i.e., the listening distance) will square the division value for a sphere, but only double the value for a cylinder.
This is why you get the two very different volume/distance relationships.
Well, I've done a bit of teaching technical stuff to non-technical folks over the years, and I came up with an easier way to describe this to my wife (who is definitely not technical
), and she said "Oh, I see now." So I thought perhaps this approach could be helpful to others.It goes like this: Sound is simply energy that comes from a speaker, and how much of that energy you receive will determine how 'loud' it is to you (i.e., the volume). Now, for a point source the energy will move out in a sphere, but for a line source it will move out in a cylinder (we'll ignore the 'ends' of the cylinder for this). Finally, the amount of energy available at any point on one of these expanding surfaces (i.e., the volume at a listening position) will be the total energy divided by the total area of that surface that it has to be 'spread over'.
Well, the surface area of a sphere is calculated as "four times PI times R-squared" (I don't know how to do equations here), where R is the radius, while the surface area for a cylinder (again, ignoring the two 'ends') is calculated as "two times R times PI times H", where R is the radius and H is the hight of the cylinder. So you can see that doubling R (i.e., the listening distance) will square the division value for a sphere, but only double the value for a cylinder.
This is why you get the two very different volume/distance relationships.
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