jQuery filling Selectbox no value on page load (timing?)

have a little issue with jquery and couldn´t find a solution yet:

when page loads there the selectbox is filled with data from my sql. but the value is "undefined".

$(document).ready(function(){
$.get("", function(data){
    $.each(data,function(i,value){
        var option =$("<option>",
                    {text : value.hersteller}
                                )
        $('#hersteller1').append(option);
    })
})
var select = $("#hersteller1 option:selected").val();
console.log(select);

so my second jquery function doesen´t work:

$('#hersteller1').on('change', function(e){
$('#modell1').empty()
var herstellerAuswahl=e.target.value; 
$.ajax({
    type: 'post',
    url:'',
    dataType: "json",
    data:{'title':herstellerAuswahl},
    success:function(data){ 
        $.each(data,function(j,value){
            var option =$("<option>",
                        {text : value.modell})
            $('#modell1').append(option);
        })
    }
})

via Chebli Mohamed