Question

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made ${\frac{1}{3}}^{rd}$ and close 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)

$17$

For close pipe fundamental frequency is $f_c=\frac{v}{4l}$

for open pipe $f_o=\frac{2}{2l}$, SO $f_o=2f_c$

Also $f_o-f_c=3$

on solving we get $f_c=3$ and $f_o=6$

When $L=l/3$

$f_o^{\prime }=\frac{v}{2l/3}=3f_o=18$

for $L=2l$

$f_c^{\prime }=\frac{v}{4\left(3l\right)}=f_c/3=1$

beats produced =$f_o^{\prime }-f_c^{\prime }=17$