High-end stereo systems sometimes display volume in units of dB, but with a twis

Question

High-end stereo systems sometimes display volume in units of dB, but with a twist-- the reference intensity Io used (in the dB scale formula) is set to the LOUDEST sound the stereo can generate, not the threshold of human hearing. If that is the case:

a.) When the stereo is turned (1/6)th of the way up, what dB will the stereo read?
(You may assume the intensity increases linearly with the volume knob-- not always the case on actual stereos.)
_?_ dB

b.) When this stereo is turned all the way up (loudest), what will it read?
_?_ dB

c.) When this stereo is turned all the way down (no sound), what will it read?

_?_

Explanation / Answer

I (in dB) = 10 log (I/Io)

a) I = Io / 6

dB = 10 log (Io/6Io) = -7.782 dB

b)

I = Io

dB = 10 log (Io/Io) = 0 dB

c) I = 0

dB = 10 log 0 = -infinity

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