To find the ratio of amplitudes, we can use the relationship between intensity and amplitude for waves. The intensity of a wave is proportional to the square of its amplitude. Mathematically, we have the following relationship:
I = k * A^2
where I is the intensity, A is the amplitude, and k is a constant.
Given that I1 = 2I2, we can write the intensities in terms of their amplitudes:
I1 = k * A1^2 I2 = k * A2^2
Dividing these two equations, we get:
I1 / I2 = (k * A1^2) / (k * A2^2) I1 / I2 = A1^2 / A2^2
Since I1 = 2I2, we can substitute this value in the equation:
2 = A1^2 / A2^2
Taking the square root of both sides, we have:
√2 = A1 / A2
Therefore, the ratio of the amplitudes A1/A2 when I1 = 2I2 is √2.