A) 13 dB
B) 7 dB
C) 19 dB
D) 27 dB
Correct Answer: A
Solution :
As we know that,\[\beta =10\log \left( \frac{{{I}_{2}}}{{{I}_{1}}} \right)\] If the actual intensity of sound is \[{{I}_{0}}.\] Then, when the intensity is I\[{{\beta }_{1}}=10\log \left( \frac{I}{{{I}_{0}}} \right)\] When the intensity is increased by a factor 20 Then,\[{{\beta }_{2}}=10\log \left( \frac{20I}{{{I}_{0}}} \right)\] Thus, change in decibels of sound \[{{\beta }_{2}}-{{\beta }_{1}}=10\log \left( \frac{20I}{{{I}_{0}}} \right)-10\log \left( \frac{I}{{{I}_{0}}} \right)\] \[=10\log \left( \frac{20I}{I} \right)=10\log 20\]\[=13dB.\]
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