If I remember correctly, Igor commented that the sounds are somehow "chained" or "connected" to notifications.
(Note: there was a request to have sounds working independently, since they have an independent tab under "settings", so these two, "notifications" and "sounds", may not work "chained" in future Avast versions.)
So, to the OP, maybe you could check / play around with your pop ups, Status Bar monitoring, and updates settings, together with sounds.
An additional suggestion:
While an Avast notification is displayed, and a sound is supposed to be heard, you could:
1_ right-click on the "Volume" icon in your tray area;
2_ open Volume Mixer;
3_ double check the volume level and mute status of the "Avast" column.
If Avast is (supposed to be) performing a sound, a column should be displayed in the Windows Volume Mixer. This column is only displayed while the sound is heard, and that's why I say that you need to wait for some notification to be displayed (and its correspondent sound to, in theory, be heard).
After you confirm that the "Avast" column in the Windows Volume Mixer is correct (say, 100%) AND NOT in mute, you should at least wait for the next notification to actually be able to test if the sound is now active and is heard.
Please let us know if something of these steps helped.