This is an example of using WordPress Image Sizes and the picture element to implement responsive images. I prefer this method over using srcset on the img tag because that method doesn't account for window resizing or server-side caching.

wp-responsive-images.php

<?php

// Put in functions.php

/**
 * Image Sizes
 */
add_image_size( 'featured', 960, 250, array( 'center', 'center' ) );
add_image_size( 'cropped', 450, 180, array( 'center', 'center' ) );

// Put in Template File (For Example, single.php)

if ( has_post_thumbnail() ) { 
  $alt = get_post_meta( get_post_thumbnail_id(), '_wp_attachment_image_alt', true ); ?>
  <picture>
    <source media="(min-width: 450px)" srcset="<?php the_post_thumbnail_url( 'featured' ); ?>">
    <img src="<?php the_post_thumbnail_url( 'cropped' ); ?>" alt="<?php echo $alt; ?>">
  </picture>
<?php } // end if ?>