Figure 23.19 shows a heterodyne metal detector being used.

Chapter 23, Problem 23.14

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Figure 23.19 shows a heterodyne metal detector being used. As Figure 23.20 illustrates, this device utilizes two capacitor/inductor oscillator circuits, A and B. Each produces its own resonant frequency, and Any difference between these frequencies is detected through earphones as a beat frequency f 0B f 0A. In the absence of any nearby metal object, the inductances LA and LB are the same, and f 0A and f 0B are identical. There is no beat frequency. When inductor B (the search coil) comes near a piece of metal, the inductance LB increases, the corresponding oscillator frequency f 0B decreases, and a beat frequency is heard. Suppose that initially each inductor is adjusted so that LB LA, and each oscillator has a resonant frequency of 855.5 kHz. Assuming that the inductance of search coil B increases by 1.000% due to a nearby piece of metal, determine the beat frequency heard through the earphones.