The circuit is very simple. It has an RC combination and an UJT (Unijunction Transistor). The speaker is at the output of the UJT. When the circuit is turned on the capacitor C1 starts charging via R1. After a certain level of charging of C1 the input of the UJT i.e. Gate is high enough to turn on the UJT and then as the resistance of the UJT gets low. The capacitor discharges rapidly via the UJT channel. Again when it is fully discharged, the UJT gets in to cutoff mode because the Gate voltage is nearly zero. Then the capacitor again charges via R1. The process repeated and oscillation goes on. One triangular wave in audio frequency range is generating at the output causing the Beep tone.
 

Circuit Diagram:-

Component Required:-

Testing:- You can always feel an audio generator into a mike input to check an AF system, but how do you check the mike? Saying "woof, woof, hallo, test" gets mighty tiring. Instead, clamp the Mike Beeper to the front of the mike with a rubber band and you’ll send continuous tone through the mike. It lets you take your time checking the mike, connecting cable, jacks, amplifiers, etc.

The beeper can be built in a small plastic case - nothing is critical. The speaker may be any size from one to three inches.