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

Let $\nu$ be frequency of the unknown source. As it gives 4 beats per second when sounded with a source of frequency 250 Hz,

   $\therefore \nu =250\pm 4=246Hzor254Hz$         

Second harmonic of this unknown source $=2\nu$ ,that is, 492 Hz or 508 Hz,  which gives 5 beats per second, when sounded with a source of frequency 513 Hz.

Therefore, unknown frequency, $\nu$ = 254 Hz.