Fundamental frequency of closed pipe is 100 Hz and that of an open pipe is 200 Hz. Match the following…
Fundamental frequency of closed pipe is 100 Hz and that of an open pipe is 200 Hz. Match the following columns and mark the correct option from the codes given below (v s = 330 m/s).
| Column I | Column II |
| --- | --- |
| (A) Length of closed pipe | (p) 0.825 m |
| (B) Length of open pipe | (q) 1.65 m |
| (C) Lowest harmonic of closed pipe which is equal to any of the harmonic of open pipe | (r) 5 m |
| | (s) None |
(a) p q s
(b) r p s
(c) p p s
(d) p q r
Solution
For closed pipe (fundamental) $100=\dfrac{v}{4l_c}$.
Thus $l_c=\dfrac{v}{400}=\dfrac{330}{400}=0.825\,$m.
For open pipe (fundamental) $200=\dfrac{v}{2l_o}$.
Thus $l_o=\dfrac{v}{400}=0.825\,$m.
Closed-pipe frequencies: 100, 300, 500,... Hz. Open-pipe frequencies: 200, 400, 600,... Hz. None match each other.
Hence A→p, B→p, C→s (option (c)).