The power output of a tuba is 0.45 W. At what distance is the sound intensity of the tuba 1.4 × 10−3 W/m2? Answer in units of m
Power radiating from a point source follows an inverse square law and is proportional to the area of surface through which the power is flowing. The energy flowing through this area is producing what is called a flux. For a point source, the energy will flow in a direction perpendicular to the surface of a sphere. The sum of all of the energy, or power, flowing through that area will equal the total energy, or power of the source as long as we are ignoring losses.
As we get further from the source, the total power remains the same,however it is spread out over an ever increasing sized sphere, thus the intensity of the power (I = P/A) reduces by the area of the sphere encompassing the source at that distance.
The area of a sphere for a given radius will be A = 4 Pi R^2.
So, if we want to know at what distance a particular power intensity will exist we rearrange the Intensity equation to get
4PiR^2 = P/I
R^2 = P/(4IPi)
R = sqrt (P/(4Ipi))
For this example:
R = sqrt (0.45 Watt)/(4X1.4X10^-3W/m^2X3.14) = sqrt(25.6 m^2)
R = 5.06 m.