It is a horrible circuit like most Instructables who are designed by 10 years old little kids who know nothing about electronics.
A 555 is supposed to use a resistor that charges and discharges the capacitor to ground at pin 2 and pin 6. It is not designed to use an LC tuned circuit.
There should NEVER be a capacitor to ground at its output pin 3 that your circuit has, because nothing limits the very fast charge and discharge currents in it. The output is supposed to switch high and low very quickly, not ramp slowly up and down.
The Instructable has an 8 ohm speaker as its load but a 555 timer is not a high current power amplifier, its maximum allowed output current is only 200mA.
A current of 200mA into 8 ohms is produced by a peak voltage of 200mA x 8 ohms= 1.6V. But the 555 with a 12V supply will try to produce a peak voltage of (12V/2) - 2.5V= 3.5V which creates an output current of 3.5V/8 ohms= 437.5mA which might destroy the poor little 555 timer.
EDIT: The Instructable says it copied the horrible circuit from talkingelectronics.com but I couldn't find it there. There were many very good but more complicated metal detector circuits there.