The First Law of Thermodynamics states that ” energy cannot be created or destroyed. ” Thus, the Wattage ( W ) in units of Joules per second ( J/s ), whether it be generated by an electric circuit, laser beam, ocean wave, falling skydiver ( drag force times drag velocity in W = Fv ), or any energy-carrying system, must be conserved as well; however, power ( like heat ) has the ability to dissipate and become less intense.
A wavefront expanding outward from a point source and carries a quantum of energy with it. Only a fraction of the energy carried by this wavefront will be implicit upon a receptor such as an eye or an ear. Therefore, only a fraction of the power generated will be received by such a source. This power per unit area is described as the Intensity ( I ) in units of units of ( W/m^2 ).
The increasing area A = ( 4*pi*r^2 ) of a spherical wavefront is proportional to the square of its distance ( r ) from a point source. Conversely, as ( r ) increases, the intensity I = P/A of a spherical wavefront diminishes inversely with the square of the radius. This is why you cannot use starlight to view a specimen under a microscope or hear a neighbor’s snoring without technological assistance. Whether the expanding wavefront consists of light or sound, the distribution of power across the wave per unit area decreases.
Consider two points in space denoted as being located some distance from a point source; point one is located at r1, and point two is located at a distance of r2. The intensity of sound at r1 is equal to I = ( P/A ) = ( P/[4*pi*r1^2] ). The same amount of power ( P ) that existed in the spherical wave at r1 is more spread out across the larger wave with a radius of r2. Therefore, if P1 = P2, then ( I1 )( 4* pi*r1^2 ) = ( I2 )( 4*pi*r2^2 ). Thus, the intensity of the wavefront at I2 = ( I1 )( r1^2 / r2^2 ). If I1 is measured at a given distance from a point source, I2 can be determined, and vice-versa.
RENAISSANCE PHYSICS 