question_answer

A closed organ pipe and an open organ pipe are tuned to the same fundamental frequency. What is the ratio of their lengths?                                                                                               [BHU M-2003]

A)  \[1:3\]                                 

B)  \[2:1\]

C)   \[2:3\]                                

D)  \[4:3\]

Correct Answer: A

Solution :

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