Inverse Square Law
If we double the radius of the sphere to 0.564 m, the surface area of the sphere quadruples because the radius is squared in the area equation (A = 4πr2). Thus our intensity will drop to one-fourth its former value. (Note, however, that the total acoustic power is still 1 W so the LW still is 120 dB.) Now an intensity change from 1 W to 0.25 W/m2 can be written as a decibel change. The acoustic intensity (i.e., the power per unit of area) has dropped 6 dB in any given area:
Therefore our LP had to also drop 6 dB and would now be approximately 114 dB.
This effect is commonly called the inverse square law change in level. Gravity, light, and many other physical effects exhibit this rate of change with varying distance from a source. Obviously, if you halve the radius, the levels all rise by 6 dB.