This article explains how to enable Gmail sound notifications with the Notifier for Gmail extension for Chrome. It includes information on enabling a pop-up notification for Gmail, and sound notifications for other email providers.
If you want to hear a new email message when you're using Gmail in your desktop web browser, you can set that up, but not in Gmail itself.
Since Gmail does not support sending sound notifications through a web browser, you will need to install a third-party program such as Notifier for Gmail (a Chrome extension).
If you use the Notifier for Gmail Chrome extension: