The sound energy absorbed by a material is 1/4th of the energy absorbed by an open window of double the area of the material in the same time. The coefficient of absorption of the material is

0.25

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0.5

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0.75

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Solution

The correct option is B 0.5
Sound energy is inversely proportional to area times coefficient of absorption.
For open window coefficient of absorption is $2$ .
Area of open window $= 2 \times$ Area of material
$E_{1} \propto \frac{1}{A_{1} \times C_{1}}; E_{2} \propto \frac{1}{A_{2} \times C_{2}}$
$\frac{E_{1}}{E_{2}} = \frac{A_{2} C_{2}}{A_{1} C_{1}}$

$C_{2} = \frac{E_{1} A_{1} C_{1}}{E_{2} A_{2}} = \frac{1 \times 2 \times 1}{4 \times 1} = 0.5$

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