Question

A tuning fork is vibrating at $250\, Hz$. The length of the shortest closed organ pipe that will resonate with the tuning fork will be ____ $cm$.
(Take speed of sound in air as $340\, ms ^{-1}$ )

Answer 1

$\frac{\lambda}{4}=\ell \Rightarrow \lambda=4 \ell$
$f =\frac{ V }{\lambda}=\frac{ V }{4 \ell}$
$\Rightarrow 250=\frac{340}{4 \ell}$
$\Rightarrow \ell=\frac{34}{4 \times 25}=0.34 \,m$
$\ell=34 \,cm$