The above metal detector circuit is said to be beat frequency oscillation type, but i am not so sure if it is true. what really happens is that the 555 timer is configured as special type of astable multivibrator, which is like a digital oscillator producing a 50% duty cycle square wave output,due to the single resistor used in the circuit (allows same time for charge and discharge of capacitor c1). this square wave is then further modified by a series resonating circuit (the search coil and the 2nd capacitor (c2)), further increasing the operating frequency of the metal detector to the audio frequency range, this causes the continuous buzzing sound heard when the device is switched on. and we all know the rest, once a metal is brought close to the coil it changes the coil frequency, which in turn changes the overall operating frequency of the system,hence changing the tone heard at the buzzer.
