First slide

Travelling wave

Question

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

Moderate

A

1 : 4
B

1 : 16
C

1 : 2
D

1 : 1

Solution

Intensity $\propto a^{2} ω^{2}$
here $\frac{a_{A}}{a_{B}} = \frac{2}{1}$ and $\frac{ω_{A}}{ω_{B}} = \frac{1}{2} \Rightarrow \frac{I_{A}}{I_{B}} = {(\frac{2}{1})}^{2} \times {(\frac{1}{2})}^{2} = \frac{1}{1}$

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