Question

we know that for a point source, Intensity is inversely proportional to r^2, but for a beam, what would be the relationship between the intensity and the distance travelled?

Answer 1

The phenomenon was called absorbtion:
The amplitude of waves decreases while they propagate through a medium. This is caused by transformation of the vibrational energy into another form of energy, for ex. heat.
Generally we can state
\[I _{1}=I _{0}.e ^{\left( -kd \right)}\]
Where k is called the absorption coefficient, d is the distance travelled, and I0 the initial amplitude, and I1 the amplitude after distance d travelled.

Hope I helped...

Answer 2

If there is no absorption(k = 0), the intensity remains constant.