The alarm circuit transmits on MW (Medium Wave) (this is the small problem with the police). IC1a, together with a sensor (try a 20cm x 20cm sheet of tin foil) oscillates at just over 1MHz. This is modulated by an audio frequency (a continuous beep) produced by 4093 CMOS IC1b. When a hand or a foot approaches the sensor, the frequency of the transmitter (CMOS IC1a) drops appreciably.
Suppose now that the alarm circuit transmits at 1MHz. Suppose also that your radio is tuned to a frequency just below this. The 1MHz transmission will therefore not be heard by the radio. But bring a hand or a foot near to the sensor, and the transmitter's frequency will drop, and a beep will be heard from the radio.
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