Sometimes you really need to focus on the game and don't want any sound at all! Here's how to turn it off for each way to play. You may also want to disable notifications! See at the bottom of the article for how to do that.
Web
From the home page, select ‘settings’ then ‘board and pieces’ and from there you can turn off the sound!
Android and IOS
Tap on 'more in the bottom right, then tap 'settings’
From the settings, select ‘board’
Within the game settings you will be able to turn off sound!
Notifications
Android:
To disable notifications, exit the app and go into your phone’s settings. From there select ‘apps & notifications’ and then select the Chess.com app.
From here, you can enable or disable notifications for the app.
IOS:
To turn off notifications or notification sounds, exit the app, and go into the iPhone's main Settings, then to Notifications, then select the Chess.com app.
From here, you can enable or disable the move-notifications, notification sounds, and badges. (By itself, the small red "badge" displays the number of games where it's your move.)