Question

The ratio of the amplitudes of two waves is 4:9. What is the ratio of their intensities\

Answer 1

Ratio of intensities = 16/81

Answer 2

The ratio of their intensities will be 16:81.

Explanation:

Let $A_1\ and\ A_2$ are the amplitudes of two waves such that they are in ratio of 4:9. We need to find the ratio of their intensities. We know that the intensity of a wave is directly proportional to the square of its amplitude.

So, $\dfrac{I_1}{I_2}=(\dfrac{A_1}{A_2})^2$

$\dfrac{I_1}{I_2}=(\dfrac{4}{9})^2$

$\dfrac{I_1}{I_2}=\dfrac{16}{81}$

So, the ratio of their intensities will be 16:81. Hence, this is the required solution.

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