Does it sound like a USB device "connect" or "disconnect" sound or something else? Open the Windows System Sounds screen and go down the list and use the test button on that screen to see if you can identify the sound.

As for the Realtek driver, manually set a System Restore point to be safe. Then open Device Manager and find the Realtek entry under Sound, video, game controllers.  Right-click and Uninstall it.

Next, click View>Show hidden devices on the Device Manager toolbar. Look everywhere in DM for any "Unknown" device(s) and Uninstall it/them too.

Now click Action>Scan for hardware changes on the toolbar and it should install the Realtek driver.

Hopefully that will eliminate the sounds you're hearing.

As I mentioned when I first started this thread, a Realtek driver update was/is needed, but it failed, and I don't know what to do about that. I will try uninstalling and reinstalling right now. Thanks.  

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@MsKarma wrote:

As I mentioned when I first started this thread, a Realtek driver update was/is needed, but it failed, and I don't know what to do about that. I will try uninstalling and reinstalling right now. Thanks.  

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I told you how you should be able to resolve the Realtek driver issue... Whether that solves the beeps is a different question...