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 The unknown frequency is

Options

A. 254 Hz
B. 246 Hz
C. 240 Hz
D. 260 Hz

Answer

A

Explanation

The given frequency is v = 250 Hz.
The probability of unknown frequency producing 4 beat/s with 250 Hz.
`v_(1) = 250 +- 4 = 254` Hz or 246 Hz
Case (i) 2nd harmonic of 254 = `2 xx 254 = 508` Hz
`therefore` 513 - 508 = 5 beats produced.
Case (ii) 2nd harmonic of 246 `= 2 xx 246` = 492 Hz
`therefore` 513 - 492 = 21 beats produced.
`therefore` The unknown frequency is 254 Hz.
Therefore, unknown frequency, `v_(1) = 254` Hz