Question

An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency $166Hz$; if the length of the air column is

• A. 0.5 m
• B. 1.0 m
• C. 1.5 m
• D. 2.0 m

Answer 1

Answer: (A)

When air is blown at the open end of a closed pipe a longitudinal wave travels in the air of the pipe from closed end to open end. When $\lambda$ is wave length and I the length of pipe and $n$ the frequency of note emitted and $v$ the velocity of sound in air, then

$n=\frac{v}{\lambda },$ (fundamental note)
Given, $n=166Hz,v=332m/s$
$\therefore$ $\lambda =\frac{332}{166}=2m$
But, $\lambda =4l$
$\therefore$ $l=\frac{\lambda }{4}=\frac{2}{4}=0.5m$