Let the array length property do the work:
myarray[myarray.length] = 'new element value added to the end of the array';
myarray.length returns the number of strings in the array.
JS is zero based so the next element key of the array will be the current length of the array.
EX:
var myarray = [0, 1, 2, 3],
myarrayLength = myarray.length; //myarrayLength is set to 4