Here are a few suggestions, which are common fixes for your audio/sound problem and are based on troubleshooting solutions found through research.
1. Sound settings. The video may have no sound because the sound has been turned off on your computer. Hover over the speaker icon on your video or on YouTube to see if there is an "X" beside the volume slider. If yes, then click to unlock it and slide it to your desired level (this works for a large part of people).
2. Sound card. Go to another site to see if there is sound in other online videos. This is for your sound card verifying. If all other videos have sound except for YouTube, then your sound card has nothing to do with the YouTube no sound problem.
3. Adobe Flash player. Check out the version of your Adobe Flash player. YouTube and many other video websites use Flash player for video playing, and Adobe Flash browser plug-in problems happen often, which, as a result, show up as no sound or audio in YouTube videos. Download the newest Adobe Flash player to have a try if you are still using the old version. Or get the previous one back if the YouTube No Sound problem appears only after you use the upgrade edition.
4. Web browser. You can also try to test the audio by using different web browsers, like IE, Chrome, Firefox, etc, which may be a solution for fixing no audio problem as well.