Final answer:
The correct statement is that intensity increases when area decreases because intensity is inversely proportional to the area over which the power of a wave is distributed. This relationship holds true in various physics contexts, including wave behavior and the photoelectric effect.
Step-by-step explanation:
When discussing the relationship between intensity, area, and energy, we must consider the physics of waves and the principles like the conservation of energy and the inverse square law. Intensity is defined as the power per unit area and is expressed as I = P/A, where I is intensity, P is power, and A is area. The correct statement among the offered choices is that intensity increases when area decreases.
The intensity indeed goes up by a factor of 4 when the amplitude doubles because of the square relationship between amplitude and intensity, without violating the conservation of energy. Additionally, the intensity decreases as the wave moves out from the source because the energy is distributed over a larger area. Even in applications like the photoelectric effect, increasing the brightness (which equates to intensity) of light increases the number of electrons ejected, providing insight into how intensity relates to other physical phenomena.
Therefore, the statements that intensity increases with a decrease in area or that intensity decreases with an increase in energy are unsupported. The second statement, which suggests that intensity increases when area decreases, is the true statement according to the inverse relationship between intensity and area.