Footer script

footer-script.php

<script>
jQuery(function($) {

  var newLogo = 'http://yoursite.com/path/to/image.jpg';
  var oldLogo = $('.site-logo').attr('src');
  var headerFix = $('.site-header').offset().top;
  
  $(window).on('load scroll', function() {
    var y = $(this).scrollTop();
    if ( y >= 107 ) {
      $('.site-logo').attr('src',newLogo);
    } else {
      $('.site-logo').attr('src',oldLogo);
    }
  });

});
</script>