Wave Mechanics Question 659
Question: The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has same frequency as first overtone of a closed organ pipe. If speed of sound is 330 m/s, then the length of closed organ pipe is
Options:
A) 41cm
B) 37cm
C) 31cm
D) 80cm
Show Answer
Answer:
Correct Answer: A
Solution:
[a] For open pipe, $ n=\frac{v}{2\ell } $ , where $ n _{0} $ is the fundamental frequency of open pipe.
$ \
Therefore ,\ell =\frac{v}{2n}=\frac{330}{2\times 300}=\frac{11}{20} $ As freq. of 1 st overtone of open pipe = freq. of 1 st overtone of closed pipe
$ \
Therefore 2\frac{v}{2\ell }=3\frac{v}{4\ell ‘} $
$ \Rightarrow \ell ‘=\frac{3\ell }{4}=\frac{3}{4}\times \frac{11}{20}=41.25cm $
BETA
