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The closed and open organ pipes have sam...

The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produces three beats. The length of open pipe is made `(1^(rd))/(3)` and closed pipe is made three 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 the open pipe , fundamental frequency ` = n_(1) = v/(2L) `
and for the first overtone , `n_(2) = 2n_(1) = v/L ` ….(1)
For the closed pipe, fundamental frequency `n_(1) = v/(4L) `
and for the first overtone `n_(2) = 3n_(1) = (3v)/(4L) ` ...(2)
`n_(2) - n_(2) = v/L - (3v)/(4L) = v/(4L) `
` :. ` Difference between the two frequencies = No. of beat /s
`:. n_(2) - n_(2) = v/(4L) = 3`
` :. v/L = 12 ` ....(3)
When the length of the open pipe is made `L/3`, the fundamental frequency
` N_(1) = v/(2(L/3)) = (3v)/(2L)`
and for the closed pipe, the length is made 3L.
` :. N_(2) = v(4(3L)) = v/(12L) `
` :. ` The beat frequency ` = N_(1) - N_(2) `
` = (3v)/(2L) - v/(12L)`
` - (18v)/(12L) - v/(12L) = (17v)/(12L)`
` = 17/12 xx 12` ...from (3)
` :. ` The beat frequency = 17 ....Option (c )
Note : We cannot hear these beats .
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