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Default help with choosing sample rate, bit rate, max bandwidth

Hi,

For some lower quality endoding of files to mp3's, I noticed
that I can choose different sample rates for the destination
file-- ie: 32000, 22000, 16000.

I encoded one file at 40kbps/22000 and then again
at 40kbps/32000.

They were both the same size after encoding.

However, the 'maximum bandwidth for the files we
32000 was 4235Hz
22000 was 6032Hz

I figured the higher bitrate would have the higher bandwidth,
but it does not--the program Cool Edit Pro, adjusted it
automatically.

What I am wondering is, how much does the sample rate effect
the quality of mp3 files? And is there a formula to calculate
proper cutoff?

And why did the bandwidth go down for a higher sample rate?

The reason I'm trying to figure this out is because I am seeking a
happy medium between smallest size possible with acceptable quality.

Thanks,
Mb

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