Question

The ratio of maximum and minimum intensity due to superposition of two waves is 49/9 then the ratio of intensity of component waves is

Answer 1

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Answer 2

Given that,

The ratio of maximum and minimum intensity due to superposition of two waves is 49:9.

To find,

The  ratio of intensity of component waves.

Solution,

Let a and b are components of the waves such that,

$\dfrac{I_{max}}{I_{min}}=\dfrac{(a+b)^2}{(a-b)^2}\\\\\dfrac(49}{9}=\dfrac{(a+b)^2}{(a-b)^2}\\\\\dfrac{7}{3}=\dfrac{(a+b)}{(a-b)}\\\\3a+3b=7a-7b\\\\\dfrac{a}{b}=\dfrac{10}{4}\\\\\dfrac{a}{b}=\dfrac{5}{2}$

Intensity is directly proportional to the square of its amplitude. So,

$\dfrac{I_1}{I_2}=\dfrac{a^2}{b^2}\\\\\dfrac{I_1}{I_2}=(\dfrac{5}{2})^2\\\\\dfrac{I_1}{I_2}=\dfrac{25}{4}$

So, the ratio of intensity of component waves is 25:4.

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