Question

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

Answer 1

Correct Answer - A
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)=259Hz` and `(508)/(2)=254Hz`
Hence unknown frequency is `254 Hz`.