The displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities IA / IB is equal to

Question

The displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities IA / IB is equal to (A) 1: 4 (B) 1: 16 (C) 1: 2 (D) 1: 1

Tardigrade Admin · Accepted Answer

Intensity propto a2 ω2 Here (aA/aB)=(2/1) and (ωA/ωB)=(1/2) ⇒ (IA/IB)=((2/1))2 ×((1/2))2=(1/1)

Q. The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $I_{A} / I_{B}$ is equal to

1 : 4

1 : 16

1 : 2

1 : 1

Intensity $\propto a^{2} ω^{2}$
Here $\frac{a _{A}}{a _{B}} = \frac{2}{1}$
and $\frac{ω _{A}}{ω _{B}} = \frac{1}{2}$
$\Rightarrow \frac{I _{A}}{I _{B}} = (\frac{2}{1})^{2} \times (\frac{1}{2})^{2} = \frac{1}{1}$

Q. The displacement-time graphs for two sound waves A and B are shown in the figure, then the ratio of their intensities IA​/IB​ is equal to