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 frequency of source is
A) $195\ Hz$
B) $205\ Hz$
C) $190\ Hz$
D) $210\ Hz$
Explanation
(b) Initially number of beats per second $= 5$
$\therefore$ Frequency of pipe $= 200 \pm 5 = 195\ Hz$ or $205\ Hz$ …(i)
Frequency of second harmonics of the pipe $= 2n$ and number of beats in this case $= 10$
$\therefore 2n = 420 \pm 10 \Rightarrow 410\ Hz$ or $430\ Hz$
$\Rightarrow n = 205\ Hz$ or $215\ Hz$ …(ii)
From equation (i) and (ii) it is clear that $n = 205\ Hz$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.