Final answer:
The circuit combining signals from an IF amplifier and a BFO to produce an audio signal is the product detector.
Step-by-step explanation:
The circuit that combines signals from an IF (Intermediate Frequency) amplifier stage and a beat-frequency oscillator (BFO) to produce an audio signal is known as a product detector. The product detector effectively mixes the IF signal with the signal from the BFO to produce an audio frequency signal that can be heard through a speaker or headphones after being amplified by an audio amplifier. This process is crucial in the operation of radios, especially in single-sideband (SSB) or morse code (CW) communications, where it allows for the conversion of a modulated carrier into an audio range signal that can be interpreted by the listener.