Fifth harmonic of an closed organ pipe matches with first overtone of an open organ pipe. Now the pipes are joined to form a closed organ pipe. Then the ratio of the fundamental frequency of the open pipe to that of the composite pipe is
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a
9 : 2
b
2 : 7
c
7 : 2
d
11 : 2
answer is A.
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Detailed Solution
(1)5.V4lC=4.V4lC ⇒ l0=45lC∴ L=length of composite pipe=lo+lc=lo+54 lo=94lo∴ Required ratio =2.V4lo1.V4L= V2lo × 4 × 9lo4V=9 : 2