Testing here in FireFox 26.0, works as expected.
When I either close the Modal or click outside of it and then re-open it - video is back to start and stopped.
EDIT 1
Reproduced in Chrome, the video indeed keeps playing after the Modal is closed.
Try these already answered questions
Stop a youtube video with jquery?
Twitter Bootstrap Modal stop Youtube video
The best way seems to be to use YouTube API to stop the video. Answer that uses this method is available in the questions above.
EDIT 2
This solution seems to be working.
First, get the JS from this post: YouTube iframe API: how do I control a iframe player that's already in the HTML?
and include it on the page.
Add this JS after you have loaded the above script (just before the closing body tag)
<script type="text/javascript">
$('#myModal').on('hidden.bs.modal', function () {
callPlayer('yt-player', 'stopVideo');
});
</script>
You will also need to add an ID to the div containing the iframe, as below
<div class="modal-body" id="yt-player">
<iframe src="//www.youtube.com/embed/sIFYPQjYhv8?rel=0&enablejsapi=1" allowfullscreen="" width="100%" frameborder="0" height="100%"></iframe>
</div>
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