Its on one of the slides in my physics lecture, but cant work out why. Think it has something to do with an 3dB increase in volume if sound is doubled, but not sure.
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the dB scale measures intensity of sound; the amplitude is proportional to the square of the intensity, so if you double amplitude, intensity increases by a factor of 2^2 or a factor of 4
now, the dB scale is a logarithmic scale, such that an increase of 10 dB represents an increase in intensity by a factor of 10
i.e., 50 dB has 10 times more intensity than 40 dB
the intensity in dB is expressed as
I in dB = 10 log[I/I0]
in our case, we are told that I/I0 = 4 since the new intensity is 4 times the old intensity
therefore,
I in dB changes by 10 log[4] = 10*0.6 = 6 dB
doubling the amplitude quadruples the intensity, which increases the dB scale by 6
now, the dB scale is a logarithmic scale, such that an increase of 10 dB represents an increase in intensity by a factor of 10
i.e., 50 dB has 10 times more intensity than 40 dB
the intensity in dB is expressed as
I in dB = 10 log[I/I0]
in our case, we are told that I/I0 = 4 since the new intensity is 4 times the old intensity
therefore,
I in dB changes by 10 log[4] = 10*0.6 = 6 dB
doubling the amplitude quadruples the intensity, which increases the dB scale by 6