Question

An open pipe is suddenly closed at one end with the result that the frequency of third harmonic of the closed pipe is termed to be higher by $ 100 \,Hz $ , than the fundamental frequency of the open pipe. The fundamental frequency of the open pipe is :

• A. $ 200 \,Hz $
• B. $ 150 \,Hz $
• C. $ 100 \,Hz $
• D. $ 250 \,Hz $

Answer 1

Answer: (A)

An open pipe forms antinode at both ends. If length of pipe is $l$ and $v$ the velocity, then the fundamental frequency is given by

$n = \frac{v}{2\,l}$
Frequency of third harmonic of closed pipe is

$n' = \frac{3\,v}{4\,l}$
Given, $nʹ − n = 100$
$\therefore \frac{3\,v}{4\,l} - \frac{v}{2\,l} = 100$
$\Rightarrow \frac{v}{4\,l} = 100$
$\Rightarrow \frac{1}{2}\left(\frac{v}{2\,l}\right) = 100$
$\therefore n = 200\, Hz$.