Final answer:
Intensity is defined as power per unit area, and the perceived change in intensity follows an inverse square law with distance. Doubling the distance from a sound source reduces the intensity to one-fourth of the original value.
Step-by-step explanation:
The fraction of the intensity by which a source of physical energy must be increased or decreased for a perceptible difference relies on the principle that intensity is inversely proportional to the square of the distance from the source. Intensity, as defined by physics, is the power per unit area and is measured in watts per square meter (W/m²). The concept that the perceived intensity change follows an inverse square relationship is crucial in understanding wave energy distribution.
This means, for instance, if the distance to the sound source is doubled, the new intensity will be (1/2)² = 1/4 of the original intensity. If a star is twice as far away compared to another of the same luminosity, it will appear four times dimmer (2 squared = 4 times less bright). Such calculations are vital in fields ranging from astronomy to acoustics.