The first obertone of an open organ pipe beats with the first overtone of a closed organ pipe with a beat frequency of 2.2 Hz. The fudamental frequency of clos3ed organ pipe is 110 Hz. Find length of the open pipe. (Given, sound in air =330 m/s )
A
2.43 m
B
0.73 m
C
0.993 m
D
2.93 m
Text Solution
Verified by Experts
The correct Answer is:
C
Funkdamental frequency of closed organ pipe, `v_(o)=v/(4l_(o))rArrL_(o)=v/(4xx110)=0.75m` Frequency of first overtone of open organ pipe, `v_(1)=2xxv/(2L_(o))=v/(L_(o))` Frequency of first overtone of closed prgan pipe, `v_(2)=3v_(o)` `=3xxv/(4L_(o))=(3xx330)/(4xx0.75)=330 Hz` `therefore" "v_(1)-v_(2)=2.2,v/(L_(o))-330=2.2` `rArr" "v/(L_(o))=332.2` `rArr" " L_(o)=(330)/(332.2)=0.993m`
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