Ratio of intensities of two waves are given by 4 : 1. Then the ratio o...
Ratio of intensities of two waves are given by 4 : 1. Then the ratio o...
Given:
Ratio of intensities of two waves = 4 : 1
To find:
Ratio of the amplitudes of the two waves
Solution:
The intensity of a wave is directly proportional to the square of its amplitude. Therefore, we can write:
Intensity ∝ (Amplitude)^2
Let the amplitudes of the two waves be A1 and A2, and their intensities be I1 and I2 respectively.
According to the given ratio of intensities:
I1 : I2 = 4 : 1
We know that intensity is directly proportional to the square of the amplitude, so we can write:
I1/I2 = (A1/A2)^2
Substituting the given ratio of intensities, we have:
4/1 = (A1/A2)^2
Taking the square root on both sides, we get:
√(4/1) = A1/A2
Simplifying the square root, we have:
2 = A1/A2
Therefore, the ratio of the amplitudes of the two waves is 2 : 1, which corresponds to option A.