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A source of unknown frequency gives 4 beats/s, when sounded with a source of known frequency 250 Hz. The second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. The unknown frequency is

1. 246 Hz
2. 240 Hz
3. 260 Hz
4. 254 Hz

Correct answer: 246 Hz

Solution

The beat frequency is the absolute difference between the frequencies of two sources. For the first case, the unknown frequency is either 250 ± 4 Hz, i.e., 246 Hz or 254 Hz. For the second harmonic, the frequency doubles, so it becomes 492 Hz or 508 Hz. Comparing with 513 Hz, the beat frequency is 5 Hz, which matches only for 246 Hz (second harmonic = 492 Hz).

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