Hi,Steve,
Since Gmail doesn't natively support pushing sound notifications through your web browser, you must install a third-party program like Notifier for Gmail (a Chrome extension) or Gmail Notifier (a Windows program).
If you're using the Notifier for Gmail Chrome extension:
Right-click the extension icon next to Chrome's navigation bar, and choose Options.
Scroll down to the Notifications section and make sure Play alert sound for new emails is selected.
Change the sound using the drop-down menu.
Exit the window when you're done. The changes are saved automatically.
If you are using Gmail Notifier for Windows:
Right-click the program in the notification area and choose Preferences.
Make sure the Sound alert option is checked.
Click Select sound file to pick a notification sound for new Gmail messages.
Gmail Notifier only supports using WAV files for the sound. If you have an MP3 or some other type of audio file that you want to use for the Gmail notification sound, run it through a free audio file converter to save it in the WAV format. - Source Lifewire.com