how to push web notification to WordPress dashboard admin?

i have been creating a WordPress sit to a customer , he receives notification in dashboard in a customized admin menu i have created but new notification only shows up when reloading the dashboard , now he asks me to make an alert sound when new notification comes so i have an idea to push web notification every time new notification arrives but i tried to do some researches and didn't find any thing does exactly what i need ,any ideas about how to start or if there is even any better way to do it??