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 <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-7r7e22x8wv9q.png" /> (A) 1:4 (B) 1:16 (C) 1:2 (D) 1:1

Tardigrade Admin · Accepted Answer

The intensity can be given by I=2π 2ρ 2A2v Hence, (IA/IB)=(fA2 AA2/fB2 AB2) (IA/IB)=((1/2))2((2/1))2 (IA/IB)=1

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

$1 : 4$

$1 : 16$

$1 : 2$

$1 : 1$

The intensity can be given by
$I = 2 π^{2} ρ^{2} A^{2} v$
Hence,
$\frac{I _{A}}{I _{B}} = \frac{f _{A}^{2} A _{A}^{2}}{f _{B}^{2} A _{B}^{2}}$
$\frac{I _{A}}{I _{B}} = (\frac{1}{2})^{2} (\frac{2}{1})^{2}$
$\frac{I _{A}}{I _{B}} = 1$

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

1:4

1:16

1:2

1:1