A few things to try:
1. Right-click on your sound/speakers icon in the system tray, select Playback Devices, go to Speakers properties (the one which is green-ticked, also disable the red ones, if any), then go to Enhancements and tick Disable all sound effects. And that's it, restart the browser and enjoy.
In short: Volume mixer -> Playback devices -> Playback tab -> Speakers properties -> Enhancements -> Disable all sound effects -> Restart browser.
2. Open Internet Explorer. Go to Tools> Internet Options.
Switch to the Advanced Tab.
Scroll down to the Multimedia sub-heading.
Make sure the box next to Play sounds in web pages is checked. Click "ok". Restart Internet Explorer. Test to see if you can hear sound online.
2. Disable any addons, (e.g. Adblock Plus, NoScript, Flash Block, Ghostery)
Also you can check if something is missing in the Audio section: HTML5test - How well does your browser support HTML5?