Yahoo Mail provides option for disabling the sound when a new chat message is received, similary Gmail has a feature which would disable sound when a new chat message is received. This can be done using the Gmail Settings link. Click the Settings link available at the top right hand corner of Gmail account. In the Settings page, navigate to Chat tab and scroll down to the sound section.
To turn off the sound when new chat messages arrive, select the radio option with label as Sounds Off.