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,   \[n'=n'\,\,'\] \[\therefore \]  \[\frac{v}{4{{l}_{1}}}=\frac{v}{2{{l}_{2}}}\] Note: A closed pipe produces only odd harmonics while an open pipe produces both even and odd harmonics.