Question

A pipe open at both ends and a pipe closed at one end have same length. The ratio of frequencies of their $P^{th}$ overtone is

• A. $\frac{p+1}{2p}$
• B. $\frac{p+1}{2p+1}$
• C. $\frac{2\left(p+1\right)}{2p+1}$
• D. $\frac{p}{2p+1}$

Answer 1

Answer: (C)

Frequency of $p$ th overtone of open organ pipe
$=(p+1) \frac{v}{2 L}$...(i)
where, $L=$ length of organ pipe and that of closed organ pipe is
$=(2 p+1) \frac{V}{4 L}$...(ii)
So, the ratio of $p$ th overtone of open to closed
$=\frac{(p+1) \frac{v}{2 L}}{(2 p+1) \frac{v}{4 L}}$ (using Eqs. (i) and (ii)
$=\frac{2(p+1)}{(2 p+1)}$