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# If the intensity is increased by a factor of 20, by how many decibels is the sound level increased?

3 years ago

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 ( 20 I/I)= 10* log 20=10*1.3010=13dB