A source of unknown frequency gives 4 beats/s when sounded with a source of known frequency 250 Hz. The…

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

Solution

Here, [Diagram shows 250 Hz branching to 254 Hz (second harmonic 508 Hz, giving 5 beats with 513 Hz) and 246 Hz (second harmonic 492 Hz, giving 21 beats with 513 Hz)] Hence, unknown frequency is $254\text{ Hz}$.

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