The energy of a wave is directly proportional to the square of its amplitude. Therefore, if the energy of a wave increased by a factor of 25, we can determine the corresponding factor by which the amplitude increased.
Let's denote the initial amplitude of the wave as A and the final amplitude as A'. Similarly, the initial energy is E, and the final energy is E'.
According to the relationship between energy and amplitude:
E = k * A^2
E' = k * A'^2
where k is a constant.
Given that the energy increased by a factor of 25, we can express this relationship as:
E' = 25 * E
Substituting the expressions for energy:
k * A'^2 = 25 * k * A^2
Simplifying:
A'^2 = 25 * A^2
Taking the square root of both sides:
A' = 5 * A
Therefore, the amplitude of the wave increased by a factor of 5 when the energy increased by a factor of 25.