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NEET2013PhysicsWaves and SoundActual

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

Options

  1. A254 ~Hz
  2. B246 ~Hz
  3. C240 ~Hz
  4. D260 ~Hz

Correct answer

A. 254 ~Hz

Step-by-step solution

Here, We know beat frequency is the difference of the frequencies of the sources. When unknown source is sounded with known source of frequency 250 Hz, it gives 4 beats/s. It means the frequency of unknown source may be 254 Hz or 246 Hz. Now second harmonic of the source of unknown frequency gives five beats per second, when sounded with a source of frequency 513 Hz. It means the frequency of unknown source may be 518 Hz or 508 Hz. ( As 518 2 =259 ~Hz and 508 2 =254 ~Hz ) Hence unknown frequency is 254 Hz.

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