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An organ pipe, open from both end produces 5 beats per second when vibrated with a source of frequency $200 \mathrm{~Hz}$. The second harmonic of the same pipes produces 10 beats per second with a source of frequency $420 \mathrm{~Hz}$. The fundamental frequency of organ pipe is
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$205 \mathrm{~Hz}$
Let the fundamental frequency of organ pipe be $\mathrm{f}$
Case I : $f=200 \pm 5=205 \mathrm{~Hz}$ or $195 \mathrm{~Hz}$
Case II : frequency of 2 nd harmonic of organ pipe $=2 \mathrm{f}$ (as is clear from the second figure) $2 \mathrm{f}=420 \pm 10$ or $\mathrm{f}=210 \pm 5$ or $\mathrm{f}=205$ or 215
Hence fundamental frequency oforgan pipe $=205 \mathrm{~Hz}$
Case I : $f=200 \pm 5=205 \mathrm{~Hz}$ or $195 \mathrm{~Hz}$
Case II : frequency of 2 nd harmonic of organ pipe $=2 \mathrm{f}$ (as is clear from the second figure) $2 \mathrm{f}=420 \pm 10$ or $\mathrm{f}=210 \pm 5$ or $\mathrm{f}=205$ or 215
Hence fundamental frequency oforgan pipe $=205 \mathrm{~Hz}$
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