How to create a Power ON-Power OFF tone
You need to trigger the sound when the alarm is armed and again when it is disarmed. Detecting the rising and falling edges of the arm/disarm signal will give you just that. This can be done with a simple XOR gate and a resistor/capacitor delay.



With both inputs LOW the XOR output is LOW and the astable (or you could use a buzzer instead) is OFF.

When the arming signal goes HIGH input A goes high immediately but the uncharged capacitor (C1) holds input B LOW. This gives a HIGH on the output (C) and turns the sound on. The capacitor charges through the resistance (R1) and after a short time (determined by the time constant R1 x C1) the input B goes HIGH and the output C goes LOW - turning the sound OFF.

No further sound is made until the systen is disarmed when the input A goes LOW.

When A goes LOW, input B is still HIGH because the capacitor is charged. The out put C will go HIGH and turn on the sound. The capacitor then discharges through R1 bring B LOW after a short time (determined by the time constant R1C1) bringing the output (C) LOW and turning OFF the sound.

If you wish to make one sound longer than the other you can add a resistor and two diodes to the delay circuit given them different time constants for rising and falling edges.

The IC is a 4070 type (quad XOR)