Without wrapping an iFrame in a second div container, this code will find all iFrames that you select and fit them to their containers. Great for dynamic content.

jQuery to Make iFrame Content Responsive

jQuery(window).load(function() {
    var $allVideos = jQuery("iframe[src^='http://www.youtube.com']"); //Find all embedded iframes from YouTube and load them into an array
    var $fluidElement = jQuery("Fluid_Width_Element").width();
    $allVideos.each(function() {
        jQuery(this).data('aspectRatio', this.height / this.width).removeAttr('height').removeAttr('width'); //Find the aspect ratio, store it, and remove the height and width attributes
        var $aspectRatio = jQuery(this).data('aspectRatio');
        jQuery(this).width($fluidElement).height($fluidElement * $aspectRatio); //Change the height and width of each iframe to fit the container
    })
    jQuery(window).resize(function() {
        var $newWidth = $fluidElement; //When the window is resized, store the new width
        $allVideos.each(function() {
            var $element = jQuery(this);
            $element.width($newWidth).height($newWidth * $element.data('aspectRatio')); //Change the height and width of each iframe to fit the container every time the window is resized
        })
    })
})