Question

An air column in a pipe which is closed at one end, will be in resonance with the vibrating body of frequency $166\, Hz$; 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=166\,Hz, v=332\,m/s $
$ \therefore $ $ \lambda =\frac{332}{166}=2\,m $
But, $ \lambda =4l $
$ \therefore $ $ l=\frac{\lambda }{4}=\frac{2}{4}=0.5\,m $