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Reflection from an Open End

In an experim...

Question

In an experiment to measure the absorption coefficient by stationary method, $i_{1}$ is the current measured due to maximum amplitude of sound and $i_{2}$ is the current due to minimum amplitude of sound, then:

a = \frac{i_{1} i_{2}}{(i_{1} + i_{2})^{2}}

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a = \frac{4 i_{1} i_{2}}{(i_{1} + i_{2})^{2}}

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a = \frac{(i_{1} - i_{2})^{2}}{(i_{1} + i_{2})^{2}}

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a = \frac{(i_{1} - i_{2})}{(i_{1} + i_{2})}

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Solution

The correct option is B $a = \frac{4 i_{1} i_{2}}{(i_{1} + i_{2})^{2}}$
If $i_{1}$ is the current measured due to maximum amplitude of sound and $i_{2}$ is the current due to minimum amplitude of sound, then absorption coefficient by stationary method is defined by,
$a = 1 - \frac{(i_{1} - i_{2})^{2}}{(i_{1} + i_{2})^{2}} = \frac{(i_{1} + i_{2})^{2} - (i_{1} - i_{2})^{2}}{(i_{1} + i_{2})^{2}} = \frac{4 i_{1} i_{2}}{(i_{1} + i_{2})^{2}}$

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