Question

The fundamental node produced by a closed organ pipe is of frequency $\upsilon$. The fundamental note produced by an open organ pipe of same length will be of frequency:

• A. $\frac{\upsilon }{2}$
• B. $\upsilon$
• C. $2\upsilon$
• D. $4\upsilon$

Answer 1

Answer: (C)

$2\upsilon$

Let $L$ be a length of the pipe,
The fundamental frequency of closed pipe is
${\upsilon }_c=\frac{\nu }{4L}$ .....(i)
where $\nu$ is the speed of sound in air.
Fundamental frequency of open pipe of same length is
${\upsilon }_o=\frac{\nu }{2L}$ .....(ii)
Dividde (ii) by (i), we get
$\frac{{\upsilon }_o}{{\upsilon }_c}=2$ or ${\upsilon }_o=2{\upsilon }_c=2\upsilon$