Use JavaScript to turn the containers css’ display-property to none. That will remove the audioplayer from memory and efficiently stopping it from streaming. I myself use jQuery for that.
Note that my code is customized and you probably can’t get the exact HTML for your page. You need to tweak the jQuery to fit your needs. I provide these just for an example.
My HTML looks like this:
<h4>Listen to my show</h4>
<div class="audioplayer_container" style="display: none">
<object>-- Here is the audio player object --</object>
<a href="#" class="player_close">[X] Close player</a>
</div>
<div class="player_open"><a href="#">Open player</a></div>
My jQuery script is in pastebin: https://pastebin.com/MbyX3m3N
I have also found it quite useful to first style all audioplayer containers in the page with “display: none” so that the user won’t have to load Flash automatically and thus making the page load faster. But that is up to you.