MP3 and bitrate

Question

So from what I know bitrate is the product of samplerate * bitdepth.

But I cant understand this:

here for example we try to create an MP3 file selecting bitrate to 320 and sample rate to 44.1khz

How can that be? I mean if the formula bitrate = samplerate * bitdepth stands true then it must be that bitdepth = bitrate/samplerate and in our case bitdepth = (320*1024)/44100 = ~7

Will it really have such a low bitdepth? if not then why not?

Also if the above is true would it be not wiser to sacrifice some samplerate in order to gain some bitdepth?

Last but not least lets assume a 128kbps MP3 track with 8bit as bitdepth the sample rate (according to the above equation) sould be 16384.

But the sound band of the music played will vary from 20 to ~20000hz how is this possible? I would assume that since 16384 samples per second are "spited" out from a soundcard playing that 128kbps file then the frequencies involved can not be higher than 16384hz

EDIT: In case my post is confusing: how the sampling rate of a file is factored into the output MP3 bitrate ?

Answer 1

Your assumption that bitrate = bitdepth * channels * samplerate is true for raw PCM encoded audio. It is not true for bitrate reduction encodings, be it lossless (as flac) or lossy (as mp3).

The samplerate and bitdepth given to an mp3 encoder are used to set up appropriately the encoder, and will be used at decoding stage to output a decoded audio with the same samplerate and bitdepth than the input audio.

The ratio between the raw PCM bitrate and the actual encoded bitrate of a lossy codec gives you a clue on how much information has been lost in the process.