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Ratio of intensities of two waves are given by 4 : 1. Then the ratio of the amplitudes of the twowaves is   [1991]
  • a)
    2 : 1
  • b)
    1 : 2
  • c)
    4 : 1
  • d)
    1 : 4
Correct answer is option 'A'. Can you explain this answer?
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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.
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