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KVPY Sample Paper KVPY Stream-SX Model Paper-20

  • question_answer
    Two sound waves A and B have intensities of \[10\frac{\mu W}{c{{m}^{2}}}\] and \[500\frac{\mu W}{c{{m}^{2}}}.\] Difference in their intensity levels is

    A) 490 dB

    B) 50 dB   

    C) 19 dB

    D) 17 dB

    Correct Answer: D

    Solution :

    Sound levels of A and B are
    \[{{\beta }_{A}}=10\log \left( \frac{{{I}_{A}}}{{{I}_{O}}} \right)\]
    \[{{\beta }_{B}}=10\log \left( \frac{{{I}_{B}}}{{{I}_{O}}} \right)\]
    \[\therefore \]\[{{\beta }_{A}}-{{\beta }_{B}}=10\left( \log \frac{{{I}_{A}}}{{{I}_{{}^\circ }}}-\log \frac{{{I}_{B}}}{{{I}_{O}}} \right)\]
    \[=10\log \left( \frac{{{I}_{B}}}{{{I}_{A}}} \right)=10\log \left( \frac{500}{10} \right)\]\[\Rightarrow \]\[{{\beta }_{A}}-{{\beta }_{B}}=10\log 50\]\[=10\times 1.70=17dB\]


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