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Waves and Sound — JEE physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceJEE physicsWaves and Sound1 Mark
MCQ
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 frequency of source is
  • A
    $195 \mathrm{~Hz}$
  • ✓
    $205 \mathrm{~Hz}$
  • C
    $190 \mathrm{~Hz}$
  • D
    $210 \mathrm{~Hz}$
✓

Answer

Correct option: B.
$205 \mathrm{~Hz}$
(b) Initially number of beats per second $=5$
$\therefore \text { Frequency of pipe }=200 \pm 5=195 \mathrm{~Hz} \text { or } 205 \mathrm{~Hz} \text {...(i)}$
Frequencyofsecondharmonics of the pipe $=2 n$ and number of beats in this case $=10$
$\therefore 2 n=420 \pm 10 \Rightarrow 410 \mathrm{~Hz} \text { or} 430\mathrm{~Hz}$
$\Rightarrow n=20\mathrm{~Hz} \text { or } 215 \mathrm{~Hz}$
From equation (i) and (ii) it is clear that $n=205 \mathrm{~Hz}$

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