Question 29: The ratio of frequencies of fundamental harmonic produced by an open pipe to that of closed pipe having the same length is :
(1) 1:3
(2) 3:1
(3) 1:2
(4) 2:1
Answer: Option (4)
Explanation:
For an open pipe of length L, the fundamental frequency is given by
f_{\text{open}}=\frac{v}{2L}.
For a closed pipe of the same length L,
the fundamental frequency is given by f_{\text{closed}}=\frac{v}{4L}.
The ratio of the fundamental frequencies is
\frac{f_{\text{open}}}{f_{\text{closed}}}=\frac{\frac{v}{2L}}{\frac{v}{4L}}.
Simplifying, \frac{f_{\text{open}}}{f_{\text{closed}}}=2.
Hence, the ratio of frequencies is 2:1.
Therefore, the correct answer is Option (4).