Hmm, does Firefox think it is playing media on those sites? Firefox should display a speaker icon on the tab when either a plugin or an HTML5 audio/video player is playing. Does the icon appear? (The icon is used to mute and unmute the tab, but it is un-muted by default.)

Next time you see this, could you check the Windows sound mixer? Right-click the speaker icon in the notification area of the task bar (over by the clock) and choose Open Volume Mixer. Then check whether any programs are making sound or might be muted. I'm attaching an older example for reference where the audio is coming from a separate program instead of Firefox (Flash protected mode).

Thank you for your response, unfortunately the mixer isn't the issue. The speaker icon shows up once I click play on videos from the sites that work and does not appear on sites that have audio playing but is not audible. I recently had some issues with a Windows update, so that is likely the source of the problem. I just find it strange that it is just affecting the Firefox and not other browsers.