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  • Help me understand! In a stationary wave pattern that forms as a result of reflection of waves from an obstacle, the ratio of amplitude at an antinode & a node is 1.5. What percentage of the energy passesacross the obstacle.

In a stationary wave pattern that forms as a result of reflection of waves from an obstacle, the ratio of amplitude at an antinode & a node is 1.5. What percentage of the energy passes across the obstacle.

  • Option 1)

    4%

  • Option 2)

    96%

  • Option 3)

    54%

  • Option 4)

    46%

 

Answers (1)

best_answer

\frac{A_{max}}{A_{min}}= \frac{A_{i}+A_{r}}{A_{i}-A_{r}}

\frac{A_{r}}{A_{i}}=\frac{1}{5}= \frac{I_{r}}{I_{i}}= \left ( \frac{A_{r}}{A_{i}} \right )^{2}= \frac{1}{25}

I_{r}= 0.04I_{i}

4\% Reflected 

so 96\% across obstacle

 

Amplitude of transmitted wave -

A_{t}= \left ( \frac{2V_{2}}{V_{1}+V_{2}} \right )A_{i}

A_{t}=  amplitude of transmitted wave

- wherein

A_{r}= amplitude of reflected wave

V_{1}\; and \; V_{2} are velocity of wave in incident and transmitted wave.

A_{i}= amplitude of incident  wave.

 

 


Option 1)

4%

This is incorrect

Option 2)

96%

This is correct

Option 3)

54%

This is incorrect

Option 4)

46%

This is incorrect

Posted by

Aadil

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