I think, You can use jquery ajax function.
http://api.jquery.com/jquery.ajax/[
^]
If you select one in select box then fire onselect event..
Something like this (pseudocode)
jquery.onselect(){
jquery.ajax(call php file containing the select query)
send html selected value to php file
}
success:get data in an array
fill the second select box using jquery or js
selectquery.php
mysql select query to fill the box
return or echo php array
design.html
<select id=""> first select box</select>
<select>empty select </select>