question_answer

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. The ratio of their lengths is:

A)  1 : 2         

B)  4 : 1

C)  1 : 4         

D)  2 : 1

Correct Answer: A

Solution :

 Frequency of fundamental note in closed pipe is \[n=\frac{v}{4l}\] ?(i) Frequency of fundamental note in open pipe is \[n\,=\frac{v}{2{{l}_{2}}}\] ?(ii) Given, \[n=n\,\] \[\therefore \] \[\frac{v}{4{{l}_{1}}}=\frac{v}{2{{l}_{2}}}\] \[\Rightarrow \] \[{{l}_{2}}:{{l}_{2}}=1:2\] Note: A closed pipe produces only odd harmonics while an open pipe produces both even and odd harmonics.