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A tuning fork of 256 Hz will resonate with a 512 Hz frequency because the latter is a harmonic of the former. Specifically, 512 Hz is the second harmonic of 256 Hz, meaning it is a whole number multiple (2x) of the fundamental frequency. When the 512 Hz frequency is present, it causes the 256 Hz fork to vibrate in sympathy, resulting in resonance. This phenomenon occurs due to the principle of resonance, where an object vibrates at its natural frequency when exposed to a matching frequency.
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