Question

If the ratio of intensities of two waves is 4 : 1, then the ratio of their amplitudes is

(A) 2 : 1

(B) 1 : 2

(C) 4 : 1

(D) 1 : 4

Answer 1

Correct option is (A) 2 : 1

We know that, the intensity (I) of a wave is directly proportional to the square of its amplitude (A²)

i.e., \(\frac{I_1}{I_2} = \frac{A_1^2}{A_2^2}\)

Given,

\( \frac{A_1^2}{A_2^2} = \frac 41\)

\( \Rightarrow\frac{A_1}{A_2} = \sqrt{\frac 41}\)

\( \Rightarrow\frac{A_1}{A_2} = \frac21\)

\( \Rightarrow{A_1}:{A_2} = 2:1\)