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Name: Rob E.
Status: other
Age: 30s
Location: N/A
Country: N/A
Date: 2001-2002

I would like to know how to convert voltage to decibels (dB). The only formula I have found is dbv=20 log 10 (v/1). Yet it gives no example and I do not understand.


This is not a formula for converting voltage to decibels. The stated formula converts VOLUME to decibels. Volume is commonly often stated in units of (average power per unit area), often called intensity.

This sort of unit poses one big problem: the average human ear can hear from an intensity of 10^-12 W/m^2 up to 1 W/m^2. This is too great a range to make the units convenient. The sound level (decibels) is a logarithmic quantity to make the scale much smaller. If we call let the threshold for hearing be zero decibels, the formula becomes

SL(dB) = 10 * log( V/Vo ).

V is volume in W/m^2. Vo is the threshold of hearing: 10^-12 W/m^2. The human ear can hear from 0 to 120 decibels.

To convert voltage put into a speaker into decibels put out depends on the individual speaker, as well as how far you are standing from the speaker when you listen. The further you stand from the speaker, the quieter it sounds and the lower the intensity entering your ear.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College

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