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The closed and open organ pipes have ...

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made thre time the original , the number of beats produced will be

A

8

B

14

C

17

D

20

Text Solution

Verified by Experts

The correct Answer is:
C
For open pipe first overtone `n_(1)=(v)/(L)`
For closed pipe first overtone `n_(L)=(3v)/(4L)`
`therefore n_(1)-n_(L)=(v)/(L)-(3v)/(4L)=3`
`therefore (v)/(4L)=3`
`therefore (v)/(L)=3`
`therefore (v)/(L)=12`
When length of open pipe is made `(L)/(3)` the fundamental frequency.
`n=(v)/(2((L)/(3)))=(3v)/(2L)`
When length of closed pipe is made 3 times, the fundamental frequency, `n=(v)/(4(3L))=(v)/(12L)`
Beats produced `=n_(1)-n_(2)'`
`=(17)/(12).(v)/(12L) xx 12=17`
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