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a simple radio receiver works without a battery. we built those in school. the electricity induced by the radio signal is enough to drive a small speaker.

Such a device is commonly called a crystal radio[1] and they truly are ridiculously simple. If you don’t need a tuner or an amplifier, which in this case was likely, the only components required to build an AM receiver are an antenna, a diode, and an earphone. The name derives from an early type of diode based on a piece of crystalline mineral, discovered by Braun in 1874[2].

[1] https://en.wikipedia.org/wiki/Crystal_radio

[2] https://en.wikipedia.org/wiki/Crystal_detector

Especially if you have a transmitter at full volume one room over, you'd be able to pick that up loud and clear on a crystal radio. I think you could make a small unpowered crystal radio using 1919 tech, since there's no amplification.

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