It sounds like you've already tried some of these steps, but I'll include them in full for completeness.
- Check if your TV is changed to the HDMI input your Chromecast is connected to.
- Make sure that the TV, sound bar, and/or receiver is not muted.
- Confirm that the device you use with Chromecast is not muted. If you're using a mobile device, press the volume buttons on the device while you're in the Google Home app. For Chromecast with Google TV: If you are casting the content, you can use your Chromecast Voice Remote to check if Chromecast is muted.
- If you are using the Chromecast with a TV and a separate AVR, sound bar, or external speakers, the audio should come out of the TV unless you have an output path from the TV to the AVR, sound bar, or external speakers (Example: a digital optical out cable or HDMI Audio Return Channel (ARC) enabled). In this scenario, if the audio comes out of the TV but not the AVR, then the issue is with the TV or AVR connection and not with Chromecast.
- Use a different HDMI device on the same HDMI input on your TV and check if audio works.
- Use a different HDMI input on your TV.
- Reboot your Chromecast.
- Unplug the TV from power and plug it back in after 1 minute.
- Check if the audio issue occurs from all apps or only when casting certain websites.
- Plug the Chromecast into a different TV, if possible and see if the issue persists.
- Factory reset your Chromecast.
Let me know how you get on!