Populating dropdowns that are based on others
Your data doesn't mean much. I would suggest an array of objects so that the data will have meaning. Also, I would not recommend naming your variables based on data type. JS doesn't have strict types. You can easily assign anything to the variable. This means your dadArray may not be an array at some point.

var dads = [
  {id: 1, name: 'Dad1'},
  {id: 2, name: 'Dad2'},
];

var sons = [
  {id: 1, dadId: 1, name: 'Son1'},
  {id: 2, dadId: 1, name: 'Son2'},
  {id: 3, dadId: 3, name: 'Son3'},
  {id: 4, dadId: 2, name: 'Son4'},
];


So your operation involves:


Populating the dads dropdown.
On dad selection, populate the sons dropdown depending on the dad.


I notice that in your code there's duplicates. Let's split them up into functions to be reusable. Based on the operations, you should have something like:

function populateDads(dads){...}
function populateSons(sons){...}


Let's start first with the dads. I would discourage using .html(). While it does work, what happens is that jQuery does not clean up after itself. Handlers that are assigned to elements that are replaced will linger on your page. Suggesting you use .empty() if your current set is the parent of the elements to remove or .remove() if your current set are the elements to remove.

$('select').empty(); // Empties the options


As far as I know, jQuery's .val() should be able to extract the value from a &lt;select&gt;. No need to find the selected &lt;option&gt; from the &lt;select&gt;. 

var selDad = $('#dadDrop').val();


If both your select boxes are static throughout the life of the page, you can simply just store their jQuery object in a variable. That way, you won't be querying the DOM every now and then.

var dadSelect = $('#dadDrop');
var sonSelect = $('#sonDrop');


There's also a neater way to construct elements in jQuery. It goes like:

$('&lt;tagName /&gt;', { attr: value });


Running with all these, the code should look like:



var dads = [
  {id: 1, name: 'Dad1'},
  {id: 2, name: 'Dad2'},
  {id: 3, name: 'Dad3'},
];

var sons = [
  {id: 1, dadId: 1, name: 'Son1'},
  {id: 2, dadId: 1, name: 'Son2'},
  {id: 3, dadId: 3, name: 'Son3'},
  {id: 4, dadId: 2, name: 'Son4'},
];

var dadSelect = $('#dadDrop');
var sonSelect = $('#sonDrop');

function populateDads(dads){
  dadSelect.empty();
  $.each(dads, function(index, dad){
    $('&lt;option /&gt;', {value: dad.id}).text(dad.name).appendTo(dadSelect);
  });
}

function populateSons(sons){
  sonSelect.empty();
  $.each(sons, function(index, son){
    $('&lt;option /&gt;', {value: son.id}).text(son.name).appendTo(sonSelect);
  });
}

dadSelect.on('change', function(){
  // .val() returns a string. Coerce the value to a number using the
  // prefix "+". Acts like parseFloat most of the time.
  var selectedDad = +dadSelect.val();
  var dadSons = sons.filter(function(son){ return son.dadId === selectedDad; });
  populateSons(dadSons);
});


populateDads(dads);

// Trigger change for first load to prepopulate children
dadSelect.trigger('change');
&lt;script src="https://ajax.googleapis.com/ajax/libs/jquery/1.11.1/jquery.min.js"&gt;&lt;/script&gt;
&lt;select id="dadDrop"&gt;&lt;/select&gt;
&lt;select id="sonDrop"&gt;&lt;/select&gt;