Question

An open and closed organ pipe have the same length. The ratio of $p^{th}$ mode of frequency of vibration of air in two pipes is

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

Answer 1

Answer: (B)

The frequency of note produced in the $p$ th mode of vibration in open pipe is
$v_{\text {open }}=\frac{p v}{2 L}$
The frequency of note produced in the $p$th mode of vibration in closed organ pipe is
$v_{\text {closed }}=\frac{(2 p-1) v}{4 L}$
$\therefore $ Ratio of $p$th mode of frequency of vibration of air in two pipes is
$\frac{v_{\text {open }}}{v_{\text {closed }}}=\frac{p v / 2 L}{(2 p-1) v / 4 L}=\frac{2 p}{2 p-1}$