The intensity of a sound wave is directly proportional to the square of its amplitude. Therefore, if the intensity of a sound is increased by a certain factor, the corresponding factor by which the amplitude changes can be determined by taking the square root of that factor.
In this case, if the intensity of the sound is increased to 25 times its initial value, we can calculate the factor by which the amplitude will change as follows:
Factor = √(Intensity final / Intensity initial) = √(25) = 5
Therefore, if the intensity of the sound is increased by 25 times, the amplitude will increase by a factor of 5, meaning it will become 5 times its initial value.