The energy carried by a wave is proportional to the square of its amplitude. Therefore, if one wave carries 5.0 times the energy of another wave, the ratio of their amplitudes can be determined by taking the square root of the energy ratio.
Let's denote the ratio of the amplitudes as A1/A2, where A1 is the amplitude of the wave carrying 5.0 times the energy and A2 is the amplitude of the other wave.
Since the energy is proportional to the square of the amplitude, we can write the following equation:
(E1/E2) = (A1^2/A2^2)
Given that (E1/E2) = 5.0, we can substitute this value into the equation:
5.0 = (A1^2/A2^2)
To solve for the ratio of the amplitudes, we can take the square root of both sides of the equation:
√5.0 = A1/A2
Therefore, the ratio of the amplitudes is approximately equal to √5.0, which is approximately 2.236.