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.