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Physics-

General

Easy

Question

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure, then the ratio of their intensities $I subscript A end subscript divided by I subscript B end subscript$ is equal to

1 : 4
1 : 16
1 : 2
1 : 1

The correct answer is: 1 : 1

Intensity $proportional to a to the power of 2 end exponent omega to the power of 2 end exponent$
Here $fraction numerator a subscript A end subscript over denominator a subscript B end subscript end fraction equals fraction numerator 2 over denominator 1 end fraction$ and $fraction numerator omega subscript A end subscript over denominator omega subscript B end subscript end fraction equals fraction numerator 1 over denominator 2 end fraction rightwards double arrow fraction numerator I subscript A end subscript over denominator I subscript B end subscript end fraction equals open parentheses fraction numerator 2 over denominator 1 end fraction close parentheses to the power of 2 end exponent cross times open parentheses fraction numerator 1 over denominator 2 end fraction close parentheses to the power of 2 end exponent equals fraction numerator 1 over denominator 1 end fraction$

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