Question

Does the sound quality differ when we change video quality in Youtube?

Answer 1

No not at all. Changing the Youtube video quality only affects video, not sound/audio quality. Also changing the video quality affects the internet data usage. More good quality means more data usage and low video quality implies less data usage.

Answer 2

No, sound quality will sometimes differ when you change video quality in YouTube. But actually the audio quality is decided by the codec. 

BTW, If you confront with YouTube playback error, you can fix the problem according to the reasons. Follow this guide on how to fix YouTube playback error.