Whining sound from gearbox maybe?

I have just bought a Nissan Almera 1.8 from 2004 with a manual transmission.
One thing i have noticed, is that it makes a slight whining sound that will pitch up with the engine speed, and then the whining will disappear when the engine speed increasing,
or if i press the clutch pedal down.

I have recorded the noise here https://instaud.io/1RR6
It also has a weird sound on cold starts, which i also recorded https://instaud.io/1TxK
what could be the problem?

Help is much appreciated!

All the best

Really dumb question, If the noise was there during the test drive why did you buy it.?

I would drain the trans and refill it with the exact lubricant specified by Nissan. My Honda Civic says to use Honda oil, which I do, but 10W30 can be used temporarily in an emergency. Who knows what the previous owners may have used?