"parecord --fix-rate" always creates wav files whose metadata say that the rate is 44.1 kHz, even though the server may assign some different rate to the source output. This happens because the wav file parameters are set before creating the stream.
The same issue probably affects --fix-channels and --fix-format too, but I didn't test that.
this case is different from paplay
for paplay, the audio file already contain rate and you can specify another rate to provide pitching effect
the rate in capture file should be equal to --rate which default to 44100Hz
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