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  4. An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency 200 Hz. The second harmonic of the same pipes produces 10 beats per second with a source of frequency 420 Hz. The fundamental frequency of organ pipe is

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Q. An organ pipe, open from both end produces $5$ beats per second when vibrated with a source of frequency $200 \,Hz$. The second harmonic of the same pipes produces $10$ beats per second with a source of frequency $420 \,Hz$. The fundamental frequency of organ pipe is

BITSATBITSAT 2020

Solution:

Let the fundamental frequency of organ pipe be $f$
Case $I : f =200 \pm 5=205\, Hz$ or $195\, Hz$
image
Case II: frequency of $2^{nd}$ harmonic of organ pipe $=2 f$
(as is clear from the second figure)
$2 f =420 \pm 10$ or $f =210 \pm 5$ or $f =205$ or $215$
Hence fundamental frequency of organ pipe $=205 \,Hz$