Do you mean that you want to save a 384 kHz sine wave, or do you mean that you want to your file to have a sample rate of 384000 Hz?
In either case, unless you have specialist hardware, the file will have to be down-sampled on playback because normal sound cards don’t go that high in the analogue domain, and speakers / headphones don’t go anywhere near that high.
if i may pop in, do you mean 384 kbps?
as in the bit-rate of the file (Data rate per second) ?
if you do, a nice MPEG-4 (.m4a) audio file would be fine at 384kbps (although a clean WAV file runs at about 1400kbps, which is a fantastic bitrate for audio, something like Dolby Digital is only about ~600kbps of compression, so a 384kbps audio file should be fine, mate)
even a mid-range mainboard/motherboard built-in audio adapter can do 96kHz these days, but 384kHz is a bit of overkill friend - just a suggestion of course. even audio studiohouses just mess around with 96kHz audio usually (most cases). this is why I am asking if you meant kbps (data rate) heh