The amplitude of a sound wave is directly related to its energy. Specifically, the energy of a sound wave is proportional to the square of its amplitude.
If the energy of a sound wave increases by 9 times, we can use this relationship to determine the corresponding change in amplitude. Let's assume the initial amplitude is "A" and the final amplitude is "A'". The initial energy is proportional to A^2, and the final energy is proportional to (A')^2.
Given that the energy increases by 9 times, we can write the equation:
(A')^2 = 9 * A^2
Taking the square root of both sides to solve for A', we have:
A' = 3 * A
This means that the final amplitude, A', is 3 times the initial amplitude, A. Therefore, the amplitude of the sound wave increases by a factor of 3 if its energy increases by 9 times.