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If you're not hearing anyone else either, then the most likely answer is that your account is a junior account. You can check this by going to your watch menu > Settings > Audio. If you are on a junior account, you will see a message saying so.
If you're not on a junior account, first check that your microphone is set to "On" in your watch menu > Settings > Audio > Microphone. You should see the sound meter reflect what Rec Room is hearing from your mic. If it still shows nothing when you speak, check the platform-specific sections below for some troubleshooting tips.
Oculus Home - gear icon at the top right > Settings > Devices > Rift headset > Audio Input in VR should be set to Rift microphone and the transmit volume should be up.
SteamVR - in the small status window click the small downward arrow next to the 'Steam VR' text > Settings > Audio > ensure your 'Set Record Device to' dropdown is set to your headset microphone.
Ensure your Windows privacy settings have your microphone enabled. Windows>privacy>microphone and "allow apps to access microphone".