# Does FFT magnitude of a sound drop to 1/10 of its value if sound level is decreased by 20dB?

I understand decibel = 20 * log (magnitude/reference value). To truly appreciate the meaning of this, if I have a single frequency tone that corresponds to a certain FFT magnitude shown on a PC that's constantly recording. If I lower the tone volume by 20 dB (say, by monitoring with a SPL meter), then I should see the FFT magnitude that's 1/10 of its previous value right?

I'm only trying to understand this from a theoretical perspective, ignoring complicating real life factors.

Thanks

-20dB corresponds to $$1/10$$ of the amplitude or $$1/100$$ of the energy. That's the same thing, since energy (all else being equal) is proportional to the square of the amplitude.

It also corresponds very roughly to about $$1/4$$ perceived loudness but that's an entirely different can of worms

• yes, I meant 1/10 of FFT amplitude. Thanks – user173729 Aug 6 '19 at 14:55