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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.

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