Question

Ratio of amplitude of two waves is 1:16. The ratio of maximum to minimum intensity when the waves interfere is:

A. 289:25

B. 1:256

C. 289:225

D. 3:1

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Answer

:

The correct option is C: $289:225$.

Given the amplitude ratio of two waves is $1:16$, let $A_1$ and $A_2$ represent the amplitudes of the two waves. Hence, we have:

$$ \frac{A_1}{A_2} = \frac{1}{16} $$

To find the ratio of maximum intensity to minimum intensity when the waves interfere, we use the formula:

$$ \frac{\text{Maximum intensity}}{\text{Minimum intensity}} = \frac{(A_1 + A_2)^2}{(A_1 - A_2)^2} $$

Substituting the given ratio:

$$ \frac{(1 + 16)^2}{(1 - 16)^2} $$

Simplify the expression by dividing both the numerator and the denominator by $A_2^2$:

$$ \frac{(17)^2}{(15)^2} = \frac{289}{225} = 289:225 $$

Thus, the ratio of maximum to minimum intensity is $289:225$.


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