Question

The displacement -time graphs for two sound waves $\text{A}$ and $\text{B}$ are shown in the figure. The ratio of their intensities $\frac{I_A}{I_B}$ is equal to

• A. $1:4$
• B. $1:16$
• C. $1:2$
• D. $1:1$

Answer 1

The correct option is D $1:1$

We know that, Intensity $\left(I\right)\propto a^2{\omega }^2$
From the data given in the graph, we can deduce that,
$\frac{a_A}{a_B}=\frac{2}{1}$ and $\frac{{\omega }_A}{{\omega }_B}=\frac{1}{2}$
So, $\frac{I_A}{I_B}=\frac{a_A^2{\omega }_A^2}{a_B^2{\omega }_B^2}={\left(\frac{2}{1}\right)}^2\times {\left(\frac{1}{2}\right)}^2=1$

Hence, option (d) is the correct answer.