How do I make specific tones with a piezo buzzer?
It's very hard to know from your question what you are having trouble with.  I have a piano and I can hit the keys, but it takes me a long time to hit them in the right order and with the right timings to create a new symphony.

Anyway, if creating the sounds is the problem, have you looked at the Tone library?

Different alarms have different sounds.  I once heard an alarm which sounded like the start of Fuer Elise, so probably the notes were E and D#.  That would make their frequencies about 330Hz and 311Hz:

void loop()
{
    tone(pin, 330, 250);
    delay(300);
    tone(pin, 311, 250);
    delay(300);
}


The sound you linked to sounds to me like it starts on a C, and slides up gradually one octave.  One octave higher is double the frequency, so this code should do that:

void loop()
{
    const int startFreq = 523;  // C5 is 523Hz

    // Start at the given freqency, and increase gradually by
    // one octave (double the frequency)
    for (int freq=startFreq ; freq&lt;= (startFreq*2) ; ++freq)
    {
        tone(pin, freq, 10);
        delay(3);
    }
}