This answer is only applicable for websites which uses Bootstrap. The responsive embed feature of the Bootstrap does the job. It is based on the width (not height) of the content.
<!-- 16:9 aspect ratio --><div class="embed-responsive embed-responsive-16by9"><iframe class="embed-responsive-item" src="http://www.youtube.com/embed/WsFWhL4Y84Y"></iframe></div>jsfiddle: http://jsfiddle.net/00qggsjj/2/