If the intensity of a sound is increased to 25 times its initial value, the corresponding increase in amplitude can be determined using the square root relationship between intensity and amplitude.
The relationship between intensity (I) and amplitude (A) is given by:
I ∝ A^2
This means that the intensity is proportional to the square of the amplitude.
If the intensity is increased by a factor of 25, we can write the equation as:
25I = A^2
To find the new amplitude (A') when the intensity is increased, we need to solve for A.
Taking the square root of both sides of the equation, we get:
√(25I) = √(A^2)
5√I = A
Therefore, when the intensity is increased to 25 times its initial value, the amplitude will increase by a factor of 5.