Question

The ratio of maximum to minimum intensity due to superposition of two waves is $\frac{49}{9}$.Then the ratio of the intensity of component waves is :-

• A. $\frac{25}{4}$
• B. $\frac{16}{25}$
• C. $\frac{4}{49}$
• D. $\frac{9}{49}$

Answer 1

The correct option is A $\frac{25}{4}$

We know$,$

$\frac{I_{max}}{I_{min}}=\frac{{\left(a+b\right)}^2}{{\left(a-b\right)}^2}$

$=\frac{49}{9}$

where $a,b$ are the amplitudes

$\frac{a+b}{a-b}=\frac{7}{3}$

$3a+3b=7a-7b$

or$,$ $4a=10b$

or$,$ $\frac{a}{b}=\frac{10}{4}=\frac{5}{2}$

also we know$,$ $\frac{I_1}{I_2}=\frac{a^2}{b^2}={\left(\frac{a}{b}\right)}^2=\frac{25}{4}$

So the intensity ratio of component waves $25:4$

Hence,

option $\left(A\right)$ is correct answer.