alarm going off when connection breaks?

[Kasper]

Here is my design for 1 resistor and 1 transistor NC (normally closed) wire alarm.  Cut the wire and the speaker turns on.

This is something I've considered making myself for gate to my yard, bicycles, etc.  I used digi-key to source the parts because they are my go to for fast and easy with lots of options, there are cheaper options though and I'm not sure how they are in Europe.

Parts List:
MPN (manufacturer part number):
Power Supply:            5V phone charger
Buzzer:                     AI-1223-TWT-5V-5-R
MOSFET N-channel:      IRLZ14PBF
Resistor - 100kohm: FMP100JR-52-100K
Perforated board:      SBBTH1508-1
Micro USB breakout:   
https://www.ebay.com/itm/2pcs-USB-Micro-B-Breakout-Signal-Board-Phone-Power-Charging-Converter-Module-/262889697457


MOSFET:
Vgs (voltage across pin G and pin S) max = +-10V.  Do not apply more than 9V across pin G and pin S.
Id max = 10A: do not apply more than 8A from pin D to pin S.  This buzzer uses 30mA aka 0.03A.

Think of a MOSFET as a switch, the main current flow is from pin D to pin S.  To turn on the switch, apply a voltage to pin G.
Different FETs operate at different voltages so the 5V this system is designed for might not be high enough to turn on others FETs like the ones you might have salvaged. 
The important parts:
Vth rating is lower than your power supply voltage, in this case, 5V.
Vgs max and Vds max ratings are higher than your power supply voltage.
Ids max is higher than your switched current, in this case 30mA or 0.03A.
It is good to have some margin on all those values, voltage spikes can increase voltage above planned voltage and running at max current requires a proper heatsink and expecting it to get hot.

When wire is connected, Vgs = 0V, MOSFET is off aka open aka no current flows from pin D to pin S.
When wire is cut, Vgs = 5V, MOSFET is on aka closed aka current flows fom pin D to pin S and buzzer makes noise.

Mechanical fuse:
I recommend some kind of mechanical fuse like alligator clip or banana plugs or in a bind, loosely twisted wire connection, to reduce the chance of it getting wrecked if someone tugs on the wire.

Perforated board:
Not needed but helpful for holding components while you connect them.

Power Supply:
I recommend using a 5V phone charger for your power supply since you probably have some lying around.  You could cut a USB cable and use the 5V and GND wires or you could use the breakout board in the parts list to get access to 5V (Vcc) and GND.
 
If you want to use a 9V battery, you'll need a different buzzer which has a voltage range that includes 9V.

[Kasper]

For my last post, if you want it to run on batteries, 4 x AA or 4 x AAA in series should provide 4 to 6 V when charged and the system should work at those levels.  4 x AAA batteries should last a bit over a year if it never gets triggered and a bit over a day if it is constantly triggered (speaker on).

[Brumby]

^^^ There is an example of what I meant ^^^

But before we take the next step - a couple of questions:

First - How adept are you with a soldering iron?  Do you have one?  If so - what sort?  (Make and model could be useful here).  The reason I ask is that your answer will influence how we suggest you approach the construction.  If you can solder a component with 3 half inch long legs that are a tenth of an inch apart, to a circuit board of some sort, then we can set something out one way.  If not, then we would need to try something different.

The second question is one of operating voltage.  This is something that will help with the design.  I suggest you procure the piezo buzzer and try it with different voltages and tell us what voltage provides the volume that suits your purpose.  If you just try various multiples of AA batteries, that should be precise enough.  If you want to have different volume levels, then we can do that too - in which case we will need to know the voltage for the loudest volume you want.

Choose whatever piezo buzzer you want - but the one I picked is a CPE-353.  Reasons: It has fly leads which gives options for connection.  It has a low-ish frequency so it won't be a piercing scream and it is slow pulsing, which will better attract attention - especially if you are a little bit distant.  (Changing sounds are more noticeable than constant sounds.)

[Kasper]

If you want a volume knob, you could connect a trimpot (variable resistor) between pins G and S on the FET in the circuit I drew in previous post.

[Brumby]

There's lots of things we could do ... but let's not scare the OP away just yet.