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If the intensity of sound in watts per square metre is I, then the intensity level in decibel (dB) is given by
dB= 10 log(I/I•),
Where the base of logarithm is 10,
I•=10^-12 watt per square metre( roughly the intensity at which audible sound can be heard)
On the decibel scale the pain threshold is 1 watt per square metre and on decibel scale is:
dB= 10 log(1 watt per square metre/10^-12 watt per square metre)
dB= 10 log ( 1/10^-12)= 10* log (10^12)=10*12=120 dB
In the given problem
dB= 10 log ( 2 I/I)= 10* log 2=10*0.3010=3.010dB
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