Picture the sound energy leaving the source every second as paint spreading over the inside of a growing balloon.
- Close to the source this energy is spread over a small sphere, so a unit patch of that sphere gets a lot of energy, and the sound feels loud.
- Far from the source the same total energy is spread over a much bigger sphere, so a unit patch gets far less energy, and the sound feels faint.
- The surface area of a sphere grows as the square of its radius, so if the distance doubles, the area becomes four times larger, and each patch of area receives one quarter of the previous energy.
This is the same inverse square law that governs light intensity from a point source and gravitational force between two masses. Moving away from a loudspeaker by a factor of 3 cuts the intensity down to 1/9 of its original value, confirming option C, inversely proportional to the square of the distance.