Question

Two sound waves given by $y_1=5sin\left(300\pi t\right)$ and $y_2=4sin\left(302\pi t\right)$ suprimose. The ratio of the maximum to minimum intensity of the sound waves will be

• A. $\frac{302}{300}$
• B. 81
• C. 9
• D. $\frac{5}{4}$

Answer 1

The correct option is B 81

Let intensities and amplitude of the two waves be $I_1$, $I_2$ and

$A_1,A_2$ respectively.

Given: $A_1=5unit$ and $A_2=4unit$

Also intensity of the sound wave $I\propto A^2$

Now $\frac{I_{max}}{I_{min}}=\frac{(\sqrt{I_1}+\sqrt{I_2}{)}^2}{(\sqrt{I_1}-\sqrt{I_2}{)}^2}$

$\frac{I_{max}}{I_{min}}=\frac{(A_1+A_2{)}^2}{(A_1-A_2{)}^2}$$=\frac{(5+4{)}^2}{(5-4{)}^2}$

$⟹\frac{I_{max}}{I_{min}}=81$