While we wait for the Due core to get the tone()/noTone() functions here's a suggestion for a very simple workaround. Just makes a short little chirp on a buzzer.
Use one of the Due's PWM pins (1 - 13) as beepPin
void beep() {
for (int x=0; x <10 ; x++ ) {
analogWrite(beepPin, 100);
delay(10);
analogWrite(beepPin, 0);
delay(10);
}
}