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) 0.5 m   

B) 1.0 m

C) 1.5 m   

D) 2.0 m

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 the closed end to the open end. When \[\lambda \]is wavelength and\[l\]is the length of pipe and D is the frequency of note emitted and v is the velocity of sound in air, then \[\upsilon =\frac{v}{\lambda },\](fundamental note)        Given, \[\upsilon =\frac{332}{166}=2m\] But, \[\lambda =4l\] \[\therefore \] \[l=\frac{\lambda }{4}=\frac{2}{4}=0.5m\]