Sound intensity is inversely proportional to the square of the distance from the sound source; that is

Question

I= k/ (r)^(2),

where I is the intensity, r is the distance from the sound source, and k is a constant.

Suppose that you are sitting a distance R from the TV, where its sound intensity is I (base 1). Now you move to a seat five times as far from the TV, a distance 5R away, where the sound intensity is I(base 2).

what is the relationship between I(base 1) & I (base 2)?

What is the relationship between the decibel levels associated with I(base 1) & I (base 2)
-Round the decibel level for I(base 2) to the nearest integer.

The decibel level for I(base 2) is about __?__dB lower than I (base 1)

Answer 1

I = k/r^2
Now replace r with 5r, and you have

I' = k/(5r)^2 = k/25r^2 = (1/25)(k/r^2)

If r is replaced with nr, then I gets scaled down by a factor of 1/n^2