question_answer

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)  0.5m          

B)  1.0m

C)  1.5m          

D)  2.0m

Correct Answer: A

Solution :

 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, \[n=166\text{ }Hz,\text{ }v=332m/s\] \[\therefore \] \[\lambda =\frac{332}{166}=2m\] But,          \[\lambda =4l\] \[\therefore \] \[l=\frac{\lambda }{4}=\frac{2}{4}=0.5m\]