Question

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three heats. The length of open pipe is made $\frac{1}{2}^{nd}$ and closed pipe is made three times the original, the number of beats produced will be

• A. 8
• B. 14
• C. 17
• D. 20

Answer 1

Answer: (C)

17

Answer 2

For close pipe fundamental frequency is $f_{c}=\frac{v}{4 l}$
for open pipe $f _{ o }=\frac{2}{2 l },$
SO$f _{ o }=2 f _{ c }$
Also $f _{0}- f _{ c }=3$
on solving we get $f _{ c }=3$ and $f _{ o }=6$
When $L =1 / 3$
$f _{ o }'=\frac{ v }{2 l / 3}=3 f _{ o }=18$
for $L =2 l$
$f _{ c }'=\frac{ v }{4(3 l )}= f _{ c } / 3=1$
beats produced $= f _{ o }'- f _{ c }'=17$