16:9 aspect ratio with fixed width

Aspect ratio is just width:height. So if you wanted to calculate the height based on a known width it is pretty straightforward.

//width=560, wanted height is 315
$('.player').parent().attr('height', 560*9/16);

I would recommend using css calc instead of jQuery for this:

width: 560px;
height: calc(560px * 9/16);